1Cademy - Solving $$9m^3 + 100m = 60m^2$$ by Factoring

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Solving $9m^3 + 100m = 60m^2$ by Factoring

Solve $9m^3 + 100m = 60m^2$ by collecting all terms on one side, factoring out the variable GCF, and then factoring the resulting trinomial.

Step 1 — Bring all terms to one side. Subtract $60m^2$ from both sides so that one side equals zero: $9m^3 - 60m^2 + 100m = 0$

Step 2 — Factor the greatest common factor first. All three terms share a common factor of $m$ . Factor it out: $m(9m^2 - 60m + 100) = 0$

Step 3 — Factor the trinomial. The trinomial $9m^2 - 60m + 100$ is a perfect square trinomial. Factor it as: $m(3m - 10)(3m - 10) = 0$

Step 4 — Apply the Zero Product Property. Set each factor equal to zero: $m = 0 \quad \text{or} \quad 3m - 10 = 0 \quad \text{or} \quad 3m - 10 = 0$

Step 5 — Solve each equation: $m = 0 \quad \text{or} \quad m = \frac{10}{3} \quad \text{or} \quad m = \frac{10}{3}$

Step 6 — Check your answers. The check is left to the reader.

The solutions are $m = 0$ and $m = \frac{10}{3}$ . This example demonstrates solving a polynomial equation by factoring out a common variable factor first, and then factoring the remaining quadratic trinomial.

Updated 2026-04-30

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