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Solving (4p+3)(4p−3)=0(4p + 3)(4p - 3) = 0 Using the Zero Product Property

Solve (4p+3)(4p−3)=0(4p + 3)(4p - 3) = 0 by applying the Zero Product Property.

Step 1 — Set each factor equal to zero: 4p+3=0extor4p−3=04p + 3 = 0 \quad ext{or} \quad 4p - 3 = 0

Step 2 — Solve each linear equation. Add/subtract the constant term, then divide by the coefficient: 4p=−3  ⟹  p=−34extor4p=3  ⟹  p=344p = -3 \implies p = -\frac{3}{4} \quad ext{or} \quad 4p = 3 \implies p = \frac{3}{4}

Step 3 — Check by substituting each value into the original equation: For p=−34p = -\frac{3}{4}: \left(4\left(-\frac{3}{4} ight) + 3 ight)\left(4\left(-\frac{3}{4} ight) - 3 ight) = (-3 + 3)(-3 - 3) = 0 \cdot (-6) = 0 ✓ For p=34p = \frac{3}{4}: \left(4\left(\frac{3}{4} ight) + 3 ight)\left(4\left(\frac{3}{4} ight) - 3 ight) = (3 + 3)(3 - 3) = 6 \cdot 0 = 0 ✓

The solutions are p=−34p = -\frac{3}{4} and p=34p = \frac{3}{4}.

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Updated 2026-04-30

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References

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OpenStax

Intermediate Algebra @ OpenStax

Ch.6 Factoring - Intermediate Algebra @ OpenStax

Algebra

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