Answer
The solution set is $\left\{-4, 10\right\}$.
Work Step by Step
Factor the trinomial by looking for the factors of $-40$ whose sum is equal to the coefficient of the middle term ($-6$).
These factors are $-10$ and $4$. This means that the factored form of the trinomial is $(n-10)(n+4)$.
Thus,
$n^2-6n-40=0
\\(n-10)(n+4)=0$
Equate each factor to 0; then, solve each equation to obtain:
$n-10=0 \text{ or } n+4=0
\\n=10 \text{ or } n=-4$
The solution set is $\left\{-4, 10\right\}$.
