Algebra Calculator with Steps
Solve algebra equations with detailed step-by-step solutions.
Equation Type
Enter Equation
Solution
x
Step-by-Step Solution
Step 1: Original equation
Step 2: Expand both sides
Distribute, expand products, and combine like terms on each side
Step 3: Move everything to the left side
Subtract the right side from both sides
Step 4: Solve for x
Move the constant to the right side, then divide both sides by 1
Step 5: Solution
Step 6: Verify by substitution
Both sides of the original equation match — the solution checks out
How it works
An algebra calculator solves for an unknown by keeping an equation balanced. Whatever you do to one side you do to the other — adding, subtracting, multiplying, or dividing — until the variable stands alone. It reverses the operations applied to the variable, in the opposite order.
Isolating a variable
Undo operations on both sides until x is alone ax + b = c → x = (c − b) ÷ a
- x
- the unknown to solve for
- a, b, c
- the known coefficients and constants
Worked example
- Solve 2x + 3 = 11
- Subtract 3: 2x = 8
- Divide by 2: x = 4
x = 4.
Good to know
- Do the same operation to both sides to keep the equation true.
- Undo in reverse order of operations: addition/subtraction first, then multiplication/division.
- Check your answer by substituting it back into the original equation.
Related Calculators
Frequently Asked Questions
How do I enter an equation?
Type the equation with one equals sign, using standard notation: 2x + 5 = 13, x^2 - 5x + 6 = 0, or 2(x - 3) = 4x + 8. Use ^ for exponents (the ² symbol also works), / for division by numbers (x/2 + 3 = 5), and write multiplication implicitly (2x) or with * (2*x). Spaces are optional.
What types of equations are supported?
Linear equations (ax + b = c, including parentheses, fractions like x/2, and variables on both sides), quadratic equations (ax² + bx + c = 0, including factored forms like (x+1)(x+2) = 0), and systems of two linear equations with two variables. Cubic and higher-degree polynomials are not supported yet.
Can I use a letter other than x as the variable?
Yes. Any single letter works — y + 5 = 12, 2t - 3 = 7, or a² - 9 = 0 all solve correctly. The calculator detects the variable automatically from your equation.
How does the calculator solve quadratic equations?
It rearranges the equation into standard form ax² + bx + c = 0, computes the discriminant Δ = b² - 4ac, and applies the quadratic formula x = (-b ± √Δ) / (2a). Δ > 0 gives two real roots, Δ = 0 gives one repeated root, and Δ < 0 gives two complex conjugate roots — each case is shown step by step.
How do I solve a system of two equations?
Select the System type and enter two linear equations in two variables, such as 2x + y = 7 and x - y = 2. The calculator converts them to standard form and solves by elimination (Cramer's rule), reporting the unique solution, "no solution" for parallel lines, or "infinite solutions" for equivalent equations.
What does "No solution" or "Infinite solutions" mean?
Some equations have no answer: x = x + 5 simplifies to 0 = 5, which is never true. Others are true for every value: x = x simplifies to 0 = 0. The calculator detects both cases and labels them clearly instead of returning a number.
Does the calculator check its answers?
Yes. Every real solution is substituted back into both sides of the original equation, and the verification appears as the final step of the step-by-step solution, so you can see that the left and right sides match.