## Intermediate Algebra: Connecting Concepts through Application

The solution set is $\left\{-2, 0, 5 \right\}$.
Simplify the equation to obtain: \begin{align*} w^3-3w^2-3w+9-7w-9&=0\\ w^3-3w^2-10w&=0 \end{align*} Factor out $w$: $$w(w^2-3w-10)=0$$ Factor the trinomial to obtain: $$w(w-5)(w+2)=0$$ Use the Zero-Product Property by equating each factor to zero, then solve each equation to obtain: \begin{align*} w&=0 &\text{or}& &w-5=0& &\text{or}& &w+2=0\\ w&=0 &\text{or}& &w=5& &\text{or}& &w=-2\\ \end{align*} Thus, the solution set is $\left\{-2, 0, 5 \right\}$.