Answer
The solutions are $n=8$ and $n=-3$.
Work Step by Step
$n^{2}-5n=24\implies n^{2}-5n-24=0$
To factor the polynomial $n^{2}+bn+c$ to $(n+p)$ and $(n+q)$, we need to have $p+q=b$ and $pq=c$.
In this case, $b=-5$ and $c=-24$.
$\implies p=-8$ and $q=3$.
Then, $n^{2}-5n-24=(n-8)(n+3)$
$n^{2}-5n-24=0\implies (n-8)(n+3)=0$
Using zero-product property, we have
$n-8=0$ or $n+3=0$
$\implies n=8$ or $n=-3$
The solutions are $n=8$ and $n=-3$.
