Answer
$$n=6,\:n=-3$$
Work Step by Step
Completing the square, we find:
$$n^2-3n-18+\left(-\frac{3}{2}\right)^2-\left(-\frac{3}{2}\right)^2 \\ \left(n-\frac{3}{2}\right)^2-\frac{81}{4}$$
Setting this equal to zero:
$$\left(n-\frac{3}{2}\right)^2=\frac{81}{4} \\ n=6,\:n=-3$$