Solve s=sqrt{v+w^3/2x}-z

$$s = \sqrt { \frac { v + w ^ { 3 } } { 2 x } } - z$$

Solve for s (complex solution)

$$s=\frac{\sqrt{\frac{2\left(w^{3}+v\right)}{x}}-2z}{2}$$

$$x\neq 0$$

Solve for v (complex solution)

$$v=2x\left(z+s\right)^{2}-w^{3}$$

$$x\neq 0\text{ and }\left(s=-z\text{ or }arg(z+s)<\pi \right)$$

Solve for s

$$s=\frac{\sqrt{\frac{2\left(w^{3}+v\right)}{x}}-2z}{2}$$

$$\left(x>0\text{ or }v\leq -w^{3}\right)\text{ and }\left(x<0\text{ or }v\geq -w^{3}\right)\text{ and }x\neq 0$$

Solve for v

$$v=2x\left(z+s\right)^{2}-w^{3}$$

$$s\geq -z\text{ and }x\neq 0$$