Solve (-2n-1)^2-m^2+1-17=0

$$( - 2 n - 1 ) ^ { 2 } - m ^ { 2 } + 1 - 17 = 0$$

Solve for m (complex solution)

$$m=-\sqrt{2n-3}\sqrt{2n+5}$$

$$m=\sqrt{2n-3}\sqrt{2n+5}$$

Solve for m

$$m=\sqrt{\left(2n-3\right)\left(2n+5\right)}$$

$$m=-\sqrt{\left(2n-3\right)\left(2n+5\right)}\text{, }n\leq -\frac{5}{2}\text{ or }n\geq \frac{3}{2}$$

Solve for n

$$n=\frac{-\sqrt{m^{2}+16}-1}{2}$$

$$n=\frac{\sqrt{m^{2}+16}-1}{2}$$