Solve e^2=1+xyzneqdz

$$e ^ { 2 } = 1 + x y z \neq d z$$

Evaluate (complex solution)

$$e^{2}=xyz+1\text{ and }xyz+1\neq dz$$

Solve for x

$$x=-\frac{1-e^{2}}{yz}$$

$$z\neq 0\text{ and }y\neq 0\text{ and }\left(z\neq \frac{e^{2}}{d}\text{ or }d=0\right)$$

Solve for z

$$z=-\frac{1-e^{2}}{xy}$$

$$\left(d=0\text{ or }x\neq -\frac{\left(1-e^{2}\right)d}{e^{2}y}\text{ or }d=xy\right)\text{ and }\left(d=0\text{ or }x\neq \frac{d}{y}\text{ or }d=xy\right)\text{ and }y\neq 0\text{ and }x\neq 0$$