Solve xyz^2/3=xyz

$$\frac{ xy { z }^{ 2 } }{ 3 } =xyz$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&z=3\text{ or }z=0\text{ or }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$xyz^{2}=3xyz$$

Subtract 3xyz from both sides.

$$xyz^{2}-3xyz=0$$

Combine all terms containing x.

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

Divide 0 by yz^{2}-3yz.

$$x=0$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&z=3\text{ or }z=0\text{ or }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$xyz^{2}=3xyz$$

Subtract 3xyz from both sides.

$$xyz^{2}-3xyz=0$$

Combine all terms containing y.

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

Divide 0 by xz^{2}-3xz.

$$y=0$$

Solve for x

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$xyz^{2}=3xyz$$

Subtract 3xyz from both sides.

$$xyz^{2}-3xyz=0$$

Combine all terms containing x.

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

Divide 0 by yz^{2}-3yz.

$$x=0$$

Solve for y

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$xyz^{2}=3xyz$$

Subtract 3xyz from both sides.

$$xyz^{2}-3xyz=0$$

Combine all terms containing y.

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

Divide 0 by xz^{2}-3xz.

$$y=0$$