Answer
The solution set is $\left\{0, 2, 5 \right\}$.
Work Step by Step
Simplify the equation to obtain:
\begin{align*}
w^3-7w^2+15w-5w&=0\\
w^3-7w^2+10w&=0
\end{align*}
Factor out $w$:
$$w(w^2-7w+10)=0$$
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 $\left\{0, 2, 5 \right\}$.
