Solve x_{2}+xy+yz=0

$$x _ { 2 } + x y + y z = 0$$

Solve for x (complex solution)

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

Steps for Solving Linear Equation

Subtract x_{2} from both sides. Anything subtracted from zero gives its negation.

$$xy+yz=-x_{2}$$

Subtract yz from both sides.

$$xy=-x_{2}-yz$$

The equation is in standard form.

$$yx=-x_{2}-yz$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{-x_{2}-yz}{y}$$

Dividing by y undoes the multiplication by y.

$$x=\frac{-x_{2}-yz}{y}$$

Divide -x_{2}-yz by y.

$$x=-z-\frac{x_{2}}{y}$$

Solve for x

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

Steps for Solving Linear Equation

Subtract x_{2} from both sides. Anything subtracted from zero gives its negation.

$$xy+yz=-x_{2}$$

Subtract yz from both sides.

$$xy=-x_{2}-yz$$

The equation is in standard form.

$$yx=-x_{2}-yz$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{-x_{2}-yz}{y}$$

Dividing by y undoes the multiplication by y.

$$x=\frac{-x_{2}-yz}{y}$$

Divide -x_{2}-yz by y.

$$x=-z-\frac{x_{2}}{y}$$

Solve for x_2

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