Solve 0=xz^2+yz

$$0=x { z }^{ 2 } +yz$$

Solve for x

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

Steps for Solving Linear Equation

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

$$xz^{2}+yz=0$$

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

$$xz^{2}=-yz$$

The equation is in standard form.

$$z^{2}x=-yz$$

Divide both sides by z^{2}.

$$\frac{z^{2}x}{z^{2}}=-\frac{yz}{z^{2}}$$

Dividing by z^{2} undoes the multiplication by z^{2}.

$$x=-\frac{yz}{z^{2}}$$

Divide -yz by z^{2}.

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

Solve for y

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

Steps for Solving Linear Equation

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

$$xz^{2}+yz=0$$

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

$$yz=-xz^{2}$$

The equation is in standard form.

$$zy=-xz^{2}$$

Divide both sides by z.

$$\frac{zy}{z}=-\frac{xz^{2}}{z}$$

Dividing by z undoes the multiplication by z.

$$y=-\frac{xz^{2}}{z}$$

Divide -xz^{2} by z.

$$y=-xz$$