Math Solver
Simplify expressions, solve linear and quadratic equations, factor, and work with fractions and trigonometry. Each step comes from a checked rule for that problem, and unsupported input is left unsolved.
Result
Enter a problem and press Solve. The answer and steps stay on this tab.
Worked examples
Algebra: 2(x + 3) + 4x
Multiply term by term: 2·x + 2·3 = 2x + 6. Combine like terms: 2x + 6 + 4x = 6x + 6. Final answer: 6x + 6.
Linear: 3x + 5 = 20
Start with 3x + 5 = 20. Move every term to the left side: 3x + 5 − (20) = 3x - 15. Combine like terms: 3x - 15 = 0. Final answer: x = 5.
No solution: 2x + 1 = 2x + 3
Start with 2x + 1 = 2x + 3. Move every term to the left side: 2x + 1 − (2x + 3) = -2. The variable terms cancel and the equation becomes -2 = 0. That statement is false, so there is no solution. Final answer: No solution.
Quadratic: x^2 − 5x + 6 = 0
Standard form is x^2 - 5x + 6 = 0. Write the equation as x^2, x, and constant terms: 1x^2 − 5x + 6 = 0. The discriminant is b² − 4ac = (-5)² − 4(1)(6) = 1. Final answer: x = 2 or x = 3.
Repeated root: x^2 + 2x + 1 = 0
Standard form is x^2 + 2x + 1 = 0. Write the equation as x^2, x, and constant terms: 1x^2 + 2x + 1 = 0. The discriminant is b² − 4ac = (2)² − 4(1)(1) = 0. Final answer: x = -1 (repeated root).
Complex roots: x^2 + 1 = 0
Standard form is x^2 + 1 = 0. Write the equation as x^2, x, and constant terms: 1x^2 + 0x + 1 = 0. The discriminant is b² − 4ac = (0)² − 4(1)(1) = -4. Final answer: x = i or x = -i.
Factor: x^2 − 9
Use the power rule on the single term x: the coefficient is raised to the 2 power and each exponent is multiplied by 2. The remaining polynomial x^2 - 9 factors by difference of squares. Check by expanding the factors: (x - 3)(x + 3) = x^2 - 9. Final answer: (x - 3)(x + 3).
Not factorable: x^2 + 1
Use the power rule on the single term x: the coefficient is raised to the 2 power and each exponent is multiplied by 2. x^2 + 1 does not factor over the integers by a common factor, a difference of squares, or a quadratic trinomial. Final answer: Not factorable over the integers.
Fractions: 1/2 + 1/3
1 ÷ 2 = 1/2. 1 ÷ 3 = 1/3. The least common denominator of 2 and 3 is 6. 1/2 = 3/6 and 1/3 = 2/6. Their sum is 5/6. Final answer: 5/6.
Exponents: x^5 / x^2
Use the power rule on the single term x: the coefficient is raised to the 5 power and each exponent is multiplied by 5. Use the power rule on the single term x: the coefficient is raised to the 2 power and each exponent is multiplied by 2. Divide by x^2: subtract the exponent of x^2. The quotient is x^3, for values that do not make the divisor zero. Final answer: x^3.
Negative exponent: 2^-3
2^(-3) = 1/2^3 = 1/8 = 1/8. Final answer: 1/8.
Trigonometry: sin(30)
The angle is 30°. sin(30°) = 1/2 exactly. Final answer: 1/2.
Undefined tangent: tan(90)
The angle is 90°. At 90°, cosine is 0, so tangent is undefined. Final answer: Undefined.
Right triangle with legs 3 and 4
Angle C is the right angle, so C = 90°. Side a is opposite A, side b is opposite B, and side c is the hypotenuse. By the Pythagorean theorem, c = √(a² + b²) = √(9 + 16) = √25 = 5. tan A = a/b = 3/4. A is not a standard 30°, 45°, or 60° angle, so A ≈ 36.8699° and B ≈ 53.1301°. These angles are approximations. Final answer: a = 3 b = 4 c = 5 A = about 36.8699° B = about 53.1301° C = 90°.
Supported operations and limits
Algebra expands products and combines like terms into a polynomial. Linear equations move every term to one side and solve ax + b = 0, including fractions and decimals stored as exact fractions. Quadratic equations use the discriminant. A perfect-square discriminant gives rational roots and a factor pair when one exists; a positive non-square discriminant gives simplified radicals plus a labeled decimal approximation; a negative discriminant gives complex roots labeled as not real.
Factorization pulls out the greatest common coefficient and shared variables, then looks for a difference of squares or an integer quadratic trinomial. The factors are expanded and compared with the original polynomial before they are shown. Fractions use exact rational arithmetic, including a least-common-denominator step for sums. Powers with whole-number exponents, including negative exponents of a single term, are simplified. Numeric square roots are reduced, and unlike radicals such as √2 + √3 are not forced together.
Trigonometry returns exact sine, cosine, and tangent for the standard angles and a decimal approximation otherwise. A right triangle uses the Pythagorean theorem when two sides are known and sine, cosine, or tangent when one side and one acute angle are known. A leg that is not shorter than the hypotenuse, or acute angles that do not add to 90°, is rejected.
The solver covers the grammar used in class 6–10 classwork: numbers, decimals, one-letter variables, pi, parentheses, powers, and the functions sin, cos, tan, and sqrt. It does not solve systems, inequalities, calculus, logarithms, or arbitrary word problems.
sin, cos, tan, and sqrt must be followed by parentheses. sin 30 and sin30 are not read as a function.
1/2x means (1/2)·x. Write 1/(2x) when x belongs in the denominator. Powers are right-associative, so 2^3^2 means 2^(3^2).
pi always means π, so the product of p and i must be written with a multiplication sign.
Division of a sum by a sum is not simplified. Factorization uses integers: a common factor, a difference of squares, or a quadratic trinomial. A polynomial outside those methods is reported as not factorable here.
Exact sine, cosine, and tangent are given for 0°, 30°, 45°, 60°, 90° and the matching angles in other quadrants. Other angles are decimal approximations. Right-triangle angles are exact when they are those special angles.
Common questions
Which problems does the Math Solver accept?
It simplifies polynomials, solves one linear equation, solves quadratic equations, factors by a common factor, difference of squares, or quadratic trinomial, does exact fraction and integer-power arithmetic, and evaluates sine, cosine, and tangent or a right triangle. Systems, inequalities, calculus, and logarithms are outside this page.
Why is 1/2x read as half of x?
Division and multiplication have the same priority and are read from left to right, so 1/2x means (1/2)·x. Write 1/(2x) when x should be in the denominator.
What does no solution mean for a linear equation?
If the variable terms cancel and the remaining statement is false, such as 0 = 2, no number satisfies the equation. If both sides are identical, every number is a solution.
When is a trigonometric value exact?
Exact values are given for 0°, 30°, 45°, 60°, 90° and the matching angles in other quadrants, including angles written with pi. Other angles are labeled as decimal approximations. Tangent is undefined when cosine is zero, including 90° and π/2.
Does factorization use real numbers or integers?
Factorization on this page is over the integers, after a constant denominator is taken out. x^2 + 1 is reported as not factorable here even though it factors with complex numbers. The quadratic tab shows those complex roots separately.
Are the steps generated for every school problem?
No. A step is shown only when this solver performed that transformation and checked the result. If the input is outside the supported grammar, the page says so instead of guessing a solution.