Answer
The solution set is $\left\{-9, 4\right\}$.
Work Step by Step
Factor the trinomial by looking for the factors of $-36$ whose sum is equal to the coefficient of the middle term ($5$).
These factors are $-4$ and $9$. This means that the factored form of the trinomial is $(n-4)(n+9)$.
Thus,
$n^2+5n-36=0
\\(n-4)(n+9)=0$
Equate each factor to 0; then, solve each equation to obtain:
$n-4=0 \text{ or } n+9=0
\\n=4 \text{ or } n=-9$
The solution set is $\left\{-9, 4\right\}$.
