1Cademy - Solving $$3p(10p + 7) = 0$$ Using the Zero Product Property

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Quadratic Equation

Example

Solving $3p(10p + 7) = 0$ Using the Zero Product Property

Solve $3p(10p + 7) = 0$ by applying the Zero Product Property. In this equation, one of the two factors is a monomial ( $3p$ ) rather than a binomial.

Step 1 — Set each factor equal to zero using the Zero Product Property:

$3p = 0 \quad \text{or} \quad 10p + 7 = 0$

Step 2 — Solve each equation. For the monomial factor, divide both sides by $3$ : $p = 0$ . For the binomial factor, subtract $7$ and then divide by $10$ :

$10p = -7 \implies p = -\frac{7}{10}$

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

For $p = 0$ : $3(0)(10(0) + 7) = 0 \cdot 7 = 0$ ✓

For $p = -\frac{7}{10}$ : $3\left(-\frac{7}{10}\right)\left(10\left(-\frac{7}{10}\right) + 7\right) = -\frac{21}{10}(0) = 0$ ✓

The solutions are $p = 0$ and $p = -\frac{7}{10}$ . When one factor is a monomial like $3p$ , setting it equal to zero immediately yields $p = 0$ as a solution. This shows that zero itself can be a solution to a quadratic equation — the variable does not need to take on a nonzero value.

Updated 2026-04-21

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OpenStax Elementary Algebra

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