Solve 2z=ysqrt{3x/n}

$$2 z = y \sqrt { \frac { 3 x } { n } }$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=\frac{3\times \left(\frac{y}{z}\right)^{2}x}{4}\text{, }&y\neq 0\text{ and }x\neq 0\text{ and }|arg(\sqrt{\frac{z^{2}}{y^{2}}}y)-arg(z)|<\pi \text{ and }z\neq 0\\n\neq 0\text{, }&\left(y=0\text{ or }x=0\right)\text{ and }z=0\end{matrix}\right.$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{4\times \left(\frac{z}{y}\right)^{2}n}{3}\text{, }&y\neq 0\text{ and }\left(z=0\text{ or }|arg(\sqrt{\frac{z^{2}}{y^{2}}}y)-arg(z)|<\pi \right)\text{ and }n\neq 0\\x\in \mathrm{C}\text{, }&z=0\text{ and }y=0\text{ and }n\neq 0\end{matrix}\right.$$

Solve for n

$$\left\{\begin{matrix}n=\frac{3\times \left(\frac{y}{z}\right)^{2}x}{4}\text{, }&\left(y<0\text{ and }z<0\text{ and }x\neq 0\right)\text{ or }\left(y>0\text{ and }z>0\text{ and }x\neq 0\right)\\n\neq 0\text{, }&z=0\text{ and }x=0\\n>0\text{, }&x\geq 0\text{ and }z=0\text{ and }y=0\\n<0\text{, }&x\leq 0\text{ and }z=0\text{ and }y=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{4\times \left(\frac{z}{y}\right)^{2}n}{3}\text{, }&\left(y<0\text{ or }z\geq 0\right)\text{ and }\left(y>0\text{ or }z\leq 0\right)\text{ and }y\neq 0\text{ and }n\neq 0\\x\geq 0\text{, }&z=0\text{ and }y=0\text{ and }n>0\\x\leq 0\text{, }&z=0\text{ and }y=0\text{ and }n<0\\x=0\text{, }&n\neq 0\text{ and }z=0\text{ and }y=0\end{matrix}\right.$$