Answer
$n=\pm i$ or $n=\pm 2i$
Work Step by Step
$(n^{2}+6)^{2}-7(n^{2}+6)+10=0\qquad$...substitute $n^{2}+6$ for $u$
$ u^{2}-7u+10=0\qquad$... solve with the Quadractic formula.
$u=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
$u=\displaystyle \frac{7\pm\sqrt{49-40}}{2}$
$u=\displaystyle \frac{7\pm\sqrt{9}}{2}$
$u=\displaystyle \frac{7\pm 3}{2}$
$u=\displaystyle \frac{7+3}{2}=\frac{10}{2}=5$ or $u=\displaystyle \frac{7-3}{2}=\frac{4}{2}=2$
Bring back $x^{2}=u$.
$n^{2}+6=5$ or $n^{2}+6=2$
$n^{2}=-1$ or $n^{2}=-4$
$n=\pm i$ or $n=\pm 2i$
