Answer
The solution set is $\left\{-4, 12\right\}$.
Work Step by Step
Factor the trinomial by looking for the factors of $-48$ whose sum is equal to the coefficient of the middle term ($-8$).
These factors are $-12$ and $4$. This means that the factored form of the trinomial is $(n-12)(n+4)$.
Thus,
$n^2-8n-48=0
\\(n-12)(n+4)=0$
Equate each factor to 0; then, solve each equation to obtain:
$n-12=0 \text{ or } n+4=0
\\n=12 \text{ or } n=-4$
The solution set is $\left\{-4, 12\right\}$.
