Solve 9*(x-4)=y*(x+2)

$$9 \times (x-4)=y \times (x+2)$$

Solve for x

$$x=\frac{2\left(y+18\right)}{9-y}$$

$$y\neq 9$$

Steps for Solving Linear Equation

Use the distributive property to multiply 9 by x-4.

$$9x-36=y\left(x+2\right)$$

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

$$9x-36=yx+2y$$

Subtract yx from both sides.

$$9x-36-yx=2y$$

Add 36 to both sides.

$$9x-yx=2y+36$$

Combine all terms containing x.

$$\left(9-y\right)x=2y+36$$

Divide both sides by -y+9.

$$\frac{\left(9-y\right)x}{9-y}=\frac{2y+36}{9-y}$$

Dividing by -y+9 undoes the multiplication by -y+9.

$$x=\frac{2y+36}{9-y}$$

Divide 36+2y by -y+9.

$$x=\frac{2\left(y+18\right)}{9-y}$$

Solve for y

$$y=\frac{9\left(x-4\right)}{x+2}$$

$$x\neq -2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 9 by x-4.

$$9x-36=y\left(x+2\right)$$

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

$$9x-36=yx+2y$$

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

$$yx+2y=9x-36$$

Combine all terms containing y.

$$\left(x+2\right)y=9x-36$$

Divide both sides by x+2.

$$\frac{\left(x+2\right)y}{x+2}=\frac{9x-36}{x+2}$$

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

$$y=\frac{9x-36}{x+2}$$

Divide -36+9x by x+2.

$$y=\frac{9\left(x-4\right)}{x+2}$$