Solve 5z5y=5x15z^2

$$5z5y=5x15 { z }^{ 2 }$$

Solve for x_15

$$\left\{\begin{matrix}x_{15}=\frac{yz_{5}}{z^{2}}\text{, }&z\neq 0\\x_{15}\in \mathrm{R}\text{, }&\left(z_{5}=0\text{ or }y=0\right)\text{ and }z=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Cancel out 5 on both sides.

$$z_{5}y=x_{15}z^{2}$$

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

$$x_{15}z^{2}=z_{5}y$$

The equation is in standard form.

$$z^{2}x_{15}=yz_{5}$$

Divide both sides by z^{2}.

$$\frac{z^{2}x_{15}}{z^{2}}=\frac{yz_{5}}{z^{2}}$$

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

$$x_{15}=\frac{yz_{5}}{z^{2}}$$

Solve for y

$$\left\{\begin{matrix}y=\frac{x_{15}z^{2}}{z_{5}}\text{, }&z_{5}\neq 0\\y\in \mathrm{R}\text{, }&\left(x_{15}=0\text{ or }z=0\right)\text{ and }z_{5}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Cancel out 5 on both sides.

$$z_{5}y=x_{15}z^{2}$$

Divide both sides by z_{5}.

$$\frac{z_{5}y}{z_{5}}=\frac{x_{15}z^{2}}{z_{5}}$$

Dividing by z_{5} undoes the multiplication by z_{5}.

$$y=\frac{x_{15}z^{2}}{z_{5}}$$