Solve xy+2yz+2xz=0

$$xy+2yz+2xz=0$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{2yz}{y+2z}\text{, }&y\neq -2z\\x\in \mathrm{R}\text{, }&z=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 2yz from both sides. Anything subtracted from zero gives its negation.

$$xy+2xz=-2yz$$

Combine all terms containing x.

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

Divide both sides by y+2z.

$$\frac{\left(y+2z\right)x}{y+2z}=-\frac{2yz}{y+2z}$$

Dividing by y+2z undoes the multiplication by y+2z.

$$x=-\frac{2yz}{y+2z}$$

Solve for y

$$\left\{\begin{matrix}y=-\frac{2xz}{x+2z}\text{, }&x\neq -2z\\y\in \mathrm{R}\text{, }&z=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 2xz from both sides. Anything subtracted from zero gives its negation.

$$xy+2yz=-2xz$$

Combine all terms containing y.

$$\left(x+2z\right)y=-2xz$$

Divide both sides by x+2z.

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

Dividing by x+2z undoes the multiplication by x+2z.

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