Solve xyz=2xz

$$xyz=2xz$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=2\text{ or }z=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 2xz from both sides.

$$xyz-2xz=0$$

Combine all terms containing x.

$$\left(yz-2z\right)x=0$$

Divide 0 by yz-2z.

$$x=0$$

Solve for y

$$\left\{\begin{matrix}\\y=2\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&z=0\text{ or }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$xzy=2xz$$

Divide both sides by xz.

$$\frac{xzy}{xz}=\frac{2xz}{xz}$$

Dividing by xz undoes the multiplication by xz.

$$y=\frac{2xz}{xz}$$

Divide 2xz by xz.

$$y=2$$