#### Answer

The solution set is $\left\{-3, 0, 7\right\}$.

#### Work Step by Step

Factor out $x$:
$$x(x^2-4x-21)=0$$
Factor the trinomial to obtain:
$$x(x-7)(x+3)=0$$
Use the Zero-Product Property by equating each factor to zero, then solve each equation to obtain:
\begin{align*}
x&=0 &\text{or}& &x-7=0& &\text{or}& &x+3=0\\
x&=0 &\text{or}& &x=7& &\text{or}& &x=-3\\
\end{align*}
Thus, the solution set is $\left\{-3, 0, 7\right\}$.