Intermediate Algebra: Connecting Concepts through Application

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