Solve (x+y)*z=zx+yx

$$( x + y ) \times z = z x + y x$$

Solve for x

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

Steps for Solving Linear Equation

Use the distributive property to multiply x+y by z.

$$xz+yz=zx+yx$$

Subtract zx from both sides.

$$xz+yz-zx=yx$$

Combine xz and -zx to get 0.

$$yz=yx$$

Swap sides so that all variable terms are on the left hand side.

$$yx=yz$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{yz}{y}$$

Dividing by y undoes the multiplication by y.

$$x=\frac{yz}{y}$$

Divide yz by y.

$$x=z$$

Solve for y

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

Steps for Solving Linear Equation

Use the distributive property to multiply x+y by z.

$$xz+yz=zx+yx$$

Subtract yx from both sides.

$$xz+yz-yx=zx$$

Subtract xz from both sides.

$$yz-yx=zx-xz$$

Combine zx and -xz to get 0.

$$yz-yx=0$$

Combine all terms containing y.

$$\left(z-x\right)y=0$$

Divide 0 by -x+z.

$$y=0$$