Solve (x+4)*(x+2y)=8x

$$( x + 4 ) \times ( x + 2 y ) = 8 x$$

Solve for y

$$y=-\frac{x\left(x-4\right)}{2\left(x+4\right)}$$

$$x\neq -4$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+4 by x+2y.

$$x^{2}+2xy+4x+8y=8x$$

Subtract x^{2} from both sides.

$$2xy+4x+8y=8x-x^{2}$$

Subtract 4x from both sides.

$$2xy+8y=8x-x^{2}-4x$$

Combine 8x and -4x to get 4x.

$$2xy+8y=4x-x^{2}$$

Combine all terms containing y.

$$\left(2x+8\right)y=4x-x^{2}$$

Divide both sides by 2x+8.

$$\frac{\left(2x+8\right)y}{2x+8}=\frac{x\left(4-x\right)}{2x+8}$$

Dividing by 2x+8 undoes the multiplication by 2x+8.

$$y=\frac{x\left(4-x\right)}{2x+8}$$

Divide x\left(4-x\right) by 2x+8.

$$y=\frac{x\left(4-x\right)}{2\left(x+4\right)}$$

Solve for x (complex solution)

$$x=\sqrt{y^{2}-12y+4}-y+2$$

$$x=-\sqrt{y^{2}-12y+4}-y+2$$

Solve for x

$$x=\sqrt{y^{2}-12y+4}-y+2$$

$$x=-\sqrt{y^{2}-12y+4}-y+2\text{, }y\geq 4\sqrt{2}+6\text{ or }y\leq 6-4\sqrt{2}$$