Solve left(x+8right)^2=(x+2)y

$${ \left(x+8 \right) }^{ 2 } =(x+2)y$$

Solve for y

$$y=\frac{\left(x+8\right)^{2}}{x+2}$$

$$x\neq -2$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+8\right)^{2}.

$$x^{2}+16x+64=\left(x+2\right)y$$

Use the distributive property to multiply x+2 by y.

$$x^{2}+16x+64=xy+2y$$

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

$$xy+2y=x^{2}+16x+64$$

Combine all terms containing y.

$$\left(x+2\right)y=x^{2}+16x+64$$

Divide both sides by x+2.

$$\frac{\left(x+2\right)y}{x+2}=\frac{\left(x+8\right)^{2}}{x+2}$$

Dividing by x+2 undoes the multiplication by x+2.

$$y=\frac{\left(x+8\right)^{2}}{x+2}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{y\left(y-24\right)}+y-16}{2}$$

$$x=\frac{-\sqrt{y\left(y-24\right)}+y-16}{2}$$

Solve for x

$$x=\frac{\sqrt{y\left(y-24\right)}+y-16}{2}$$

$$x=\frac{-\sqrt{y\left(y-24\right)}+y-16}{2}\text{, }y\geq 24\text{ or }y\leq 0$$