Solve x^2+6x=y(x-6)

$$x ^ { 2 } + 6 x = y ( x - 6 )$$

Solve for y

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

$$x\neq 6$$

Steps for Solving Linear Equation

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

$$x^{2}+6x=yx-6y$$

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

$$yx-6y=x^{2}+6x$$

Combine all terms containing y.

$$\left(x-6\right)y=x^{2}+6x$$

Divide both sides by x-6.

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

Dividing by x-6 undoes the multiplication by x-6.

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

Solve for x (complex solution)

$$x=\frac{\sqrt{y^{2}-36y+36}+y-6}{2}$$

$$x=\frac{-\sqrt{y^{2}-36y+36}+y-6}{2}$$

Solve for x

$$x=\frac{\sqrt{y^{2}-36y+36}+y-6}{2}$$

$$x=\frac{-\sqrt{y^{2}-36y+36}+y-6}{2}\text{, }y\geq 12\sqrt{2}+18\text{ or }y\leq 18-12\sqrt{2}$$