logo
How it worksCoursesResearch CommunitiesBenefitsAbout Us
Schedule Demo
Learn Before
Example

Solving (3m−2)(2m+1)=0(3m - 2)(2m + 1) = 0 Using the Zero Product Property

Solve (3m−2)(2m+1)=0(3m - 2)(2m + 1) = 0 by applying the Zero Product Property.

Step 1 — Set each factor equal to zero: 3m−2=0extor2m+1=03m - 2 = 0 \quad ext{or} \quad 2m + 1 = 0

Step 2 — Solve each linear equation. Add/subtract the constant term, then divide by the coefficient: 3m=2  ⟹  m=23extor2m=−1  ⟹  m=−123m = 2 \implies m = \frac{2}{3} \quad ext{or} \quad 2m = -1 \implies m = -\frac{1}{2}

Step 3 — Check by substituting each value into the original equation: For m=23m = \frac{2}{3}: \left(3 \cdot \frac{2}{3} - 2 ight)\left(2 \cdot \frac{2}{3} + 1 ight) = (2 - 2)\left(\frac{4}{3} + 1 ight) = 0 \cdot \frac{7}{3} = 0 ✓ For m=−12m = -\frac{1}{2}: \left(3\left(-\frac{1}{2} ight) - 2 ight)\left(2\left(-\frac{1}{2} ight) + 1 ight) = \left(-\frac{3}{2} - 2 ight)(-1 + 1) = -\frac{7}{2} \cdot 0 = 0 ✓

The solutions are m=23m = \frac{2}{3} and m=−12m = -\frac{1}{2}.

0

1

Updated 2026-04-30

Contributors are:

Claude Opus
Claude Opus
🏆 2

Who are from:

Claude
Claude
🏆 2

References

Tags

OpenStax

Intermediate Algebra @ OpenStax

Ch.6 Factoring - Intermediate Algebra @ OpenStax

Algebra

Related