1Cademy - Solving $$3c^2 = 10c

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How to Solve a Quadratic Equation Using the Zero Product Property

Example

Solving $3c^2 = 10c - 8$ by Factoring

Solve the quadratic equation $3c^2 = 10c - 8$ by applying the factoring method.

Step 1 — Write in standard form. Subtract $10c$ and add $8$ to both sides: $3c^2 - 10c + 8 = 0$

Step 2 — Factor the quadratic expression. $(3c - 4)(c - 2) = 0$

Step 3 — Apply the Zero Product Property. Set each factor equal to zero: $3c - 4 = 0 \quad \text{or} \quad c - 2 = 0$

Step 4 — Solve each linear equation: $c = \frac{4}{3} \quad \text{or} \quad c = 2$

Step 5 — Check both solutions by substituting into the original equation $3c^2 = 10c - 8$ : For $c = \frac{4}{3}$ : $3\left(\frac{4}{3}\right)^2 = 3\left(\frac{16}{9}\right) = \frac{16}{3}$ and $10\left(\frac{4}{3}\right) - 8 = \frac{40}{3} - \frac{24}{3} = \frac{16}{3}$ ✓ For $c = 2$ : $3(2)^2 = 12$ and $10(2) - 8 = 20 - 8 = 12$ ✓ The solutions are $c = \frac{4}{3}$ and $c = 2$ .

Updated 2026-05-25

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OpenStax Intermediate Algebra

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