$s=\frac{2\left(z+2\right)}{eto^{2}z^{4}}$
$o\neq 0\text{ and }z\neq 0\text{ and }t\neq 0\text{ and }z\neq -2$

$o=-\frac{it^{-\frac{1}{2}}\left(es\right)^{-\frac{1}{2}}\sqrt{-2z-4}}{z^{2}}$
$o=\frac{it^{-\frac{1}{2}}\left(es\right)^{-\frac{1}{2}}\sqrt{-2z-4}}{z^{2}}\text{, }z\neq 0\text{ and }t\neq 0\text{ and }s\neq 0\text{ and }z\neq -2$

$o=\frac{\sqrt{\frac{2\left(z+2\right)}{est}}}{z^{2}}$
$o=-\frac{\sqrt{\frac{2\left(z+2\right)}{est}}}{z^{2}}\text{, }\left(z\neq 0\text{ and }t>0\text{ and }s>0\text{ and }z>-2\right)\text{ or }\left(z\neq 0\text{ and }s<0\text{ and }t<0\text{ and }z>-2\right)\text{ or }\left(t<0\text{ and }s>0\text{ and }z<-2\right)\text{ or }\left(s<0\text{ and }t>0\text{ and }z<-2\right)$