Answer
The solution set is $\left\{-2, -\frac{3}{2}, 0 \right\}$.
Work Step by Step
Simplify the equation to obtain:
\begin{align*}
10x^3+30x^2+40x+15+5x^2-10x-15&=0\\
10x^3+35x^2+30x&=0
\end{align*}
Factor out $5x$:
$$5x(2x^2+7x+6)=0$$
Factor the trinomial to obtain:
$$5x(2x+3)(x+2)=0$$
Use the Zero-Product Property by equating each factor to zero, then solve each equation to obtain:
\begin{align*}
5x&=0 &\text{or}& &2x+3=0& &\text{or}& &x+2=0\\
x&=0 &\text{or}& &2x=-3& &\text{or}& &x=-2\\
x&=0 &\text{or}& &x=-\frac{3}{2}& &\text{or}& &x=-2\\
\end{align*}
Thus, the solution set is $\left\{-2, -\frac{3}{2}, 0 \right\}$.
