Solve 6(x-6)=y(x-z)

$$6(x-6)=y(x-z)$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{yz-36}{6-y}\text{, }&y\neq 6\\x\in \mathrm{R}\text{, }&z=6\text{ and }y=6\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6 by x-6.

$$6x-36=y\left(x-z\right)$$

Use the distributive property to multiply y by x-z.

$$6x-36=yx-yz$$

Subtract yx from both sides.

$$6x-36-yx=-yz$$

Add 36 to both sides.

$$6x-yx=-yz+36$$

Combine all terms containing x.

$$\left(6-y\right)x=-yz+36$$

The equation is in standard form.

$$\left(6-y\right)x=36-yz$$

Divide both sides by -y+6.

$$\frac{\left(6-y\right)x}{6-y}=\frac{36-yz}{6-y}$$

Dividing by -y+6 undoes the multiplication by -y+6.

$$x=\frac{36-yz}{6-y}$$

Solve for y

$$\left\{\begin{matrix}y=\frac{6\left(x-6\right)}{x-z}\text{, }&x\neq z\\y\in \mathrm{R}\text{, }&x=6\text{ and }z=6\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6 by x-6.

$$6x-36=y\left(x-z\right)$$

Use the distributive property to multiply y by x-z.

$$6x-36=yx-yz$$

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

$$yx-yz=6x-36$$

Combine all terms containing y.

$$\left(x-z\right)y=6x-36$$

Divide both sides by x-z.

$$\frac{\left(x-z\right)y}{x-z}=\frac{6x-36}{x-z}$$

Dividing by x-z undoes the multiplication by x-z.

$$y=\frac{6x-36}{x-z}$$

Divide -36+6x by x-z.

$$y=\frac{6\left(x-6\right)}{x-z}$$