Algebra Calculator
Examples – tap to try:
Type an equation or expression
and tap Solve.
Algebra Calculator – Solve Equations Step by Step
This free algebra calculator solves equations and simplifies expressions and shows every step of the working. Type an equation such as 3(x − 2) = 2x + 5 and it expands brackets, collects like terms, moves everything to one side and solves for x. It handles linear equations, quadratic equations (with the discriminant and quadratic formula, exact fractions and surds, and complex roots), fractions and decimals, and it can expand and simplify expressions like (2x − 1)³. A third mode solves a system of two linear equations in x and y.
It is designed for school and college students, parents helping with homework and anyone who needs to check an answer quickly. All the maths is done with exact fractions, so answers like 13/2 are shown exactly, not as a rounded decimal.
How to Use the Algebra Calculator
- Choose a mode: Solve equation, Simplify, or 2 equations.
- Type your equation or expression. Use x (or any single letter) for the unknown, ^ for powers, * or nothing for multiplication (2x, 3(x+1)), / for division and brackets as needed.
- Tap "Solve" or press Enter.
- Read the answer and the steps. Tap any example chip to see how it works.
What You Can Type
| You want | Type |
|---|---|
| Multiplication | 2x, 3(x+1), (x+1)(x−2) or 2*x |
| Division / fractions | x/2, (x+1)/3, 1/3 |
| Powers | x^2, (x+1)^3 or x² |
| Decimals | 0.5x − 1.25 = 2 |
| Other letters | 5 = 2y − 3, 3a + 2a |
The calculator works with one unknown at a time (except in the 2-equation mode). It can divide by numbers but not by expressions containing the variable, and it solves equations up to power 2.
Solving Linear Equations
A linear equation has the unknown only to the power 1, like 2x + 3 = 11. The method is to get all the x terms on one side and the numbers on the other:
- Expand any brackets: 3(x − 2) = 2x + 5 becomes 3x − 6 = 2x + 5.
- Collect x terms on one side: 3x − 2x = 5 + 6, so x − 11 = 0.
- Solve: x = 11.
- Check by substituting: 3(11 − 2) = 27 and 2(11) + 5 = 27 ✓
An equation can also have no solution (x + 1 = x + 2) or infinitely many solutions (2(x + 3) = 2x + 6). The calculator tells you which.
Solving Quadratic Equations
A quadratic equation has the form ax² + bx + c = 0. The calculator uses the quadratic formula:
x = (−b ± √(b² − 4ac)) ÷ 2a
The discriminant D = b² − 4ac tells you what kind of roots to expect:
- D > 0 – two different real roots (x² − 5x + 6 = 0 gives x = 3 or x = 2).
- D = 0 – one repeated real root (x² + 2x + 1 = 0 gives x = −1).
- D < 0 – no real roots; the roots are complex (x² + 4 = 0 gives x = 2i or x = −2i).
When D is not a perfect square, the calculator shows the exact surd form as well as decimals – for example x² − 6x + 4 = 0 gives x = 3 ± √5 ≈ 5.236 or 0.764.
Simplifying and Expanding Expressions
In Simplify mode the calculator multiplies out brackets and collects like terms. Examples:
| Expression | Simplified |
|---|---|
| (x + 2)(x − 3) | x² − x − 6 |
| 2(3x − 4) − (x + 5) | 5x − 13 |
| (x + 1)² | x² + 2x + 1 |
| (2x − 1)³ | 8x³ − 12x² + 6x − 1 |
| x/2 + x/3 | (5/6)x |
| (x − 1)(x + 1)(x² + 1) | x⁴ − 1 |
Solving Two Equations (Simultaneous Equations)
In the 2-equation mode, enter the coefficients of a₁x + b₁y = c₁ and a₂x + b₂y = c₂. The calculator uses Cramer's rule: it finds the determinant D = a₁b₂ − b₁a₂, then x = Dx ÷ D and y = Dy ÷ D. For 2x + 3y = 12 and x − y = 1 the answer is x = 3, y = 2. If D = 0 the lines are parallel (no solution) or identical (infinitely many solutions).
Frequently Asked Questions
Does the algebra calculator show steps?
Yes. Every answer comes with the step-by-step working: simplifying both sides, moving terms, the discriminant and formula for quadratics, or Cramer's rule for two equations.
Can it solve quadratic equations?
Yes. It solves any equation that simplifies to ax² + bx + c = 0, including those with fractions, and shows real, repeated or complex roots.
Can it solve cubic equations?
Not yet. Solving works for linear and quadratic equations. You can still expand and simplify cubic and higher expressions in Simplify mode.
How do I type x squared?
Type x^2, use the x² button, or paste x². For higher powers use ^, for example x^3.
Can I use letters other than x?
Yes. Any single letter works, such as y, a or t, as long as you use only one letter in an equation.
Are the answers exact?
Yes. The calculator uses exact fractions, so 0.5x − 1.25 = 2 gives x = 13/2 (6.5). Irrational roots are shown in surd form and as decimals.
Is it free?
Yes, completely free with no sign-up. Everything runs in your browser.