Solve -3xy=zxy^2

$$-3xy=zx { y }^{ 2 }$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&\left(y=-\frac{3}{z}\text{ and }z\neq 0\right)\text{ or }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract zxy^{2} from both sides.

$$-3xy-zxy^{2}=0$$

Reorder the terms.

$$-3xy-xzy^{2}=0$$

Combine all terms containing x.

$$\left(-3y-zy^{2}\right)x=0$$

Divide 0 by -3y-zy^{2}.

$$x=0$$

Solve for y

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y=-\frac{3}{z}\text{, }&z\neq 0\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$