Solve 4xy+2x+2y+2=x

$$4xy+2x+2y+2=x$$

Solve for x

$$x=-\frac{2\left(y+1\right)}{4y+1}$$

$$y\neq -\frac{1}{4}$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$4xy+2x+2y+2-x=0$$

Combine 2x and -x to get x.

$$4xy+x+2y+2=0$$

Subtract 2y from both sides. Anything subtracted from zero gives its negation.

$$4xy+x+2=-2y$$

Subtract 2 from both sides.

$$4xy+x=-2y-2$$

Combine all terms containing x.

$$\left(4y+1\right)x=-2y-2$$

Divide both sides by 4y+1.

$$\frac{\left(4y+1\right)x}{4y+1}=\frac{-2y-2}{4y+1}$$

Dividing by 4y+1 undoes the multiplication by 4y+1.

$$x=\frac{-2y-2}{4y+1}$$

Divide -2y-2 by 4y+1.

$$x=-\frac{2\left(y+1\right)}{4y+1}$$

Solve for y

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

$$x\neq -\frac{1}{2}$$

Steps for Solving Linear Equation

Subtract 2x from both sides.

$$4xy+2y+2=x-2x$$

Combine x and -2x to get -x.

$$4xy+2y+2=-x$$

Subtract 2 from both sides.

$$4xy+2y=-x-2$$

Combine all terms containing y.

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

Divide both sides by 4x+2.

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

Dividing by 4x+2 undoes the multiplication by 4x+2.

$$y=\frac{-x-2}{4x+2}$$

Divide -x-2 by 4x+2.

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