Answer
The solution set is $\left\{-\frac{7}{2}, 0, 1\right\}$.
Work Step by Step
Factor out $n$:
$$n(2n^2+5n-7)=0$$
Factor the trinomial to obtain:
$$n(2n+7)(n-1)=0$$
Use the Zero-Product Property by equating each factor to zero, then solve each equation to obtain:
\begin{align*}
n&=0 &\text{or}& &2n+7=0& &\text{or}& &n-1=0\\
n&=0 &\text{or}& &2n=-7& &\text{or}& &n=1\\
n&=0 &\text{or}& &n=-\frac{7}{2}& &\text{or}& &n=1\\
\end{align*}
Thus, the solution set is $\left\{-\frac{7}{2}, 0, 1\right\}$.
