Answer
The solutions are $n=-2$ or $n=-14$.
Work Step by Step
$ n^{2}+16n+64=36\qquad$ ...write left side as a binomial squared. ($64=8^{2}$)
$(n+8)^{2}=36\qquad$ ...take square roots of each side.
$ n+8=\pm 6\qquad$ ...add $-8$ to each side.
$ n+8-8=\pm 6-8\qquad$ ...simplify.
$ n=-8\pm 6\qquad$ ...write as separate equations.
$n=-8+6$ or $ n=-8-6\qquad$ ...simplify.
$n=-2$ or $n=-14$
