Solve (x+1)(y-2)=12

$$( x + 1 ) ( y - 2 ) = 12$$

Solve for x

$$x=-\frac{y-14}{y-2}$$

$$y\neq 2$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+1 by y-2.

$$xy-2x+y-2=12$$

Subtract y from both sides.

$$xy-2x-2=12-y$$

Add 2 to both sides.

$$xy-2x=12-y+2$$

Add 12 and 2 to get 14.

$$xy-2x=14-y$$

Combine all terms containing x.

$$\left(y-2\right)x=14-y$$

Divide both sides by y-2.

$$\frac{\left(y-2\right)x}{y-2}=\frac{14-y}{y-2}$$

Dividing by y-2 undoes the multiplication by y-2.

$$x=\frac{14-y}{y-2}$$

Solve for y

$$y=\frac{2\left(x+7\right)}{x+1}$$

$$x\neq -1$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+1 by y-2.

$$xy-2x+y-2=12$$

Add 2x to both sides.

$$xy+y-2=12+2x$$

Add 2 to both sides.

$$xy+y=12+2x+2$$

Add 12 and 2 to get 14.

$$xy+y=14+2x$$

Combine all terms containing y.

$$\left(x+1\right)y=14+2x$$

The equation is in standard form.

$$\left(x+1\right)y=2x+14$$

Divide both sides by x+1.

$$\frac{\left(x+1\right)y}{x+1}=\frac{2x+14}{x+1}$$

Dividing by x+1 undoes the multiplication by x+1.

$$y=\frac{2x+14}{x+1}$$

Divide 14+2x by x+1.

$$y=\frac{2\left(x+7\right)}{x+1}$$