Answer
The solution set is $\left\{-2, 0, 5 \right\}$.
Work Step by Step
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 $\left\{-2, 0, 5 \right\}$.