Solve xy=xxy

$$x y = x x y$$

Solve for y (complex solution)

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=1\text{ or }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$xy=x^{2}y$$

Subtract x^{2}y from both sides.

$$xy-x^{2}y=0$$

Reorder the terms.

$$xy-yx^{2}=0$$

Combine all terms containing y.

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

Divide 0 by x-x^{2}.

$$y=0$$

Solve for y

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y\in \mathrm{R}\text{, }&x=1\text{ or }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$xy=x^{2}y$$

Subtract x^{2}y from both sides.

$$xy-x^{2}y=0$$

Reorder the terms.

$$xy-yx^{2}=0$$

Combine all terms containing y.

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

Divide 0 by x-x^{2}.

$$y=0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=1\text{; }x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}\\x=1\text{; }x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$