Zero Product Property - Algebra Step by Step

Solve a quadratic by factoring and applying the zero product property: if (x+a)(x+b)=0 then x=-a or x=-b. Verify each root by substituting back into the original equation.

Example

Factor the quadratic and set each factor equal to zero.

highlighted = computed this step

Step 1 — Set up

Set up the expression.

x^{2} + 5x + 6 = 0

Step 2 — Factor

Factor the trinomial using 2 and 3.

(x+ \hl{2} )(x+ \hl{3} )= 0

Step 3 — Set factors to zero

Set each factor to zero: x + 2 = 0 and x + 3 = 0.

x+ 2 = \hl{0} \quad x+ 3 = \hl{0}

Step 4 — Roots

Read the roots: x = -2 or x = -3.

x= \hl{-2} \quad \text{or}\quad x= \hl{-3}

zero-product If a product equals zero, at least one factor must be zero. Factor the quadratic, set each factor to zero, and solve.