Solve (x-2)(y+3)=6

$$( x - 2 ) ( y + 3 ) = 6$$

Solve for x

$$x=\frac{2\left(y+6\right)}{y+3}$$

$$y\neq -3$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-2 by y+3.

$$xy+3x-2y-6=6$$

Add 2y to both sides.

$$xy+3x-6=6+2y$$

Add 6 to both sides.

$$xy+3x=6+2y+6$$

Add 6 and 6 to get 12.

$$xy+3x=12+2y$$

Combine all terms containing x.

$$\left(y+3\right)x=12+2y$$

The equation is in standard form.

$$\left(y+3\right)x=2y+12$$

Divide both sides by y+3.

$$\frac{\left(y+3\right)x}{y+3}=\frac{2y+12}{y+3}$$

Dividing by y+3 undoes the multiplication by y+3.

$$x=\frac{2y+12}{y+3}$$

Divide 12+2y by y+3.

$$x=\frac{2\left(y+6\right)}{y+3}$$

Solve for y

$$y=-\frac{3\left(x-4\right)}{x-2}$$

$$x\neq 2$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-2 by y+3.

$$xy+3x-2y-6=6$$

Subtract 3x from both sides.

$$xy-2y-6=6-3x$$

Add 6 to both sides.

$$xy-2y=6-3x+6$$

Add 6 and 6 to get 12.

$$xy-2y=12-3x$$

Combine all terms containing y.

$$\left(x-2\right)y=12-3x$$

Divide both sides by x-2.

$$\frac{\left(x-2\right)y}{x-2}=\frac{12-3x}{x-2}$$

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

$$y=\frac{12-3x}{x-2}$$

Divide 12-3x by x-2.

$$y=\frac{3\left(4-x\right)}{x-2}$$