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Algebra

From linear equations to polynomial systems — exact symbolic solutions with every step shown. Type your problem in plain English, standard notation, or LaTeX.

Solve a Algebra problem →

What Zeretis can solve

Zeretis handles the full range of algebra problems — from simple one-variable equations through to systems of nonlinear equations, partial fractions, and polynomial root-finding. Every result is exact and symbolic, never a decimal approximation.

Linear equations

Single-variable and multi-variable. Solve for any unknown, rearrange, isolate.

Quadratic equations

Factoring, quadratic formula, completing the square — all three methods available.

Polynomial equations

Higher-degree polynomials, rational roots, synthetic division, exact root forms.

Systems of equations

Two or more equations, solved simultaneously by substitution or elimination.

Factoring expressions

Factor over the integers, factor completely, identify common factors and special forms.

Partial fractions

Decompose rational expressions into partial fractions — useful for integration and signal processing.

Inequalities

Solve linear and quadratic inequalities, express solution sets in interval notation.

Simplification

Simplify algebraic expressions, cancel common factors, expand products.

How to type algebra problems

Zeretis accepts plain English descriptions, standard mathematical notation, and LaTeX. Here are examples of each:

Plain English
solve x squared minus 5x plus 6 equals 0
x = 2 or x = 3
Standard notation
x^2 - 5x + 6 = 0
x = 2 or x = 3
Plain English — system
solve the system: 2x + y = 7 and x - y = 1
x = 8/3, y = 5/3
Plain English — factoring
factor x cubed minus 8
(x − 2)(x² + 2x + 4)
Partial fractions
partial fractions of (3x + 5) / (x^2 + 3x + 2)
2/(x+1) + 1/(x+2)

What the output looks like

Every algebra solution includes a full breakdown of the method used. For a quadratic like x² − 5x + 6 = 0, you'd see:

Step-by-step output
Step 1 — Identify method: expression is factorable over the integers
Step 2 — Find factors: numbers multiplying to 6 and adding to −5 are −2 and −3
Step 3 — Factor: (x − 2)(x − 3) = 0
Step 4 — Zero-product property: x = 2 or x = 3
x = 2 or x = 3

The method label at each step tells you the rule being applied — useful for understanding the process, not just copying the answer.

Best practices

  • Use = for equations and := to define a variable before using it elsewhere
  • For systems, state each equation clearly: "solve 2x + y = 7 and x - y = 1"
  • To specify which variable to solve for: "solve 2x + 3y = 12 for y"
  • For factoring, say "factor completely" to ensure the solver goes all the way
  • For partial fractions, the denominator must be factorable — the solver will tell you if it isn't
  • Rational coefficients work fine: "solve (3/4)x + 2 = 5"
  • Complex roots are returned in exact form: a + bi

Ready to try it?

Open the solver and type any problem in plain English. Exact step-by-step answers, instantly.

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