Answer
The solution set is $\left\{-4, 0, 4\right\}$.
Work Step by Step
Add $-16n$ to both sides to obtain:
$n^3-16n=0$
Factor out $n$ to obtain:
$n(n^2-16)=0
\\n(n^2-4^2)=0$
RECALL:
A difference of two squares can be factored using the formula:
$a^2-b^2=(a-b)(a+b)$
Factor the difference of two squares to obtain:
$n(n-4)(n+4)=0$
Equate each factor to 0 then solve each equation to find:
$n=0 \text{ or } n-4=0 \text{ or } n+4 = 0\\\
n=0 \text{ or } n=4 \text{ or } n=-4$
The solution set is $\left\{-4, 0, 4\right\}$.
