## Intermediate Algebra: Connecting Concepts through Application

The solution set is $\left\{-2, -\frac{3}{2}, 0 \right\}$.
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 $\left\{-2, -\frac{3}{2}, 0 \right\}$.