1Cademy - Solving $$(x + 1)(x - 4) = 0$$ Using the Zero Product Property

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Quadratic Equation

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Solving $(x + 1)(x - 4) = 0$ Using the Zero Product Property

Solve $(x + 1)(x - 4) = 0$ by applying the Zero Product Property in three steps.

Step 1 — Set each factor equal to zero. Because the product $(x + 1)(x - 4)$ equals zero, the Zero Product Property guarantees that at least one of the two factors must be zero:

$x + 1 = 0 \quad \text{or} \quad x - 4 = 0$

Step 2 — Solve each linear equation. Each equation involves a single operation on the variable:

$x = -1 \quad \text{or} \quad x = 4$

Step 3 — Check both solutions by substituting each value back into the original equation:

For $x = -1$ : $(-1 + 1)(-1 - 4) = (0)(-5) = 0$ ✓

For $x = 4$ : $(4 + 1)(4 - 4) = (5)(0) = 0$ ✓

Both values produce a true statement, confirming that the solutions are $x = -1$ and $x = 4$ . Notice that each solution makes exactly one of the two factors equal to zero, but the product is zero in both cases.

Updated 2026-04-21

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OpenStax Elementary Algebra

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