Solve x(2y)+2x(z)=x(x(y+z))

$$x(2y)+2x(z)=x(x(y+z))$$

Solve for y

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

Steps for Solving Linear Equation

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

$$x\times 2y+2xz=x^{2}\left(y+z\right)$$

Use the distributive property to multiply x^{2} by y+z.

$$x\times 2y+2xz=x^{2}y+x^{2}z$$

Subtract x^{2}y from both sides.

$$x\times 2y+2xz-x^{2}y=x^{2}z$$

Subtract 2xz from both sides.

$$x\times 2y-x^{2}y=x^{2}z-2xz$$

Combine all terms containing y.

$$\left(x\times 2-x^{2}\right)y=x^{2}z-2xz$$

The equation is in standard form.

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

Divide both sides by 2x-x^{2}.

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

Dividing by 2x-x^{2} undoes the multiplication by 2x-x^{2}.

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

Divide xz\left(-2+x\right) by 2x-x^{2}.

$$y=-z$$

Solve for x

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