Solve xy+3x+3y-6=x

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

Solve for x

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

$$y\neq -2$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$xy+3x+3y-6-x=0$$

Combine 3x and -x to get 2x.

$$xy+2x+3y-6=0$$

Subtract 3y from both sides. Anything subtracted from zero gives its negation.

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

Add 6 to both sides.

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

Combine all terms containing x.

$$\left(y+2\right)x=-3y+6$$

The equation is in standard form.

$$\left(y+2\right)x=6-3y$$

Divide both sides by y+2.

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

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

$$x=\frac{6-3y}{y+2}$$

Divide -3y+6 by y+2.

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

Solve for y

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

$$x\neq -3$$

Steps for Solving Linear Equation

Subtract 3x from both sides.

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

Combine x and -3x to get -2x.

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

Add 6 to both sides.

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

Combine all terms containing y.

$$\left(x+3\right)y=-2x+6$$

The equation is in standard form.

$$\left(x+3\right)y=6-2x$$

Divide both sides by x+3.

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

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

$$y=\frac{6-2x}{x+3}$$

Divide -2x+6 by x+3.

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