Solve 4xy+2y=x-6

$$4xy+2y=x-6$$

Solve for x

$$x=-\frac{2\left(y+3\right)}{4y-1}$$

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

Steps for Solving Linear Equation

Subtract x from both sides.

$$4xy+2y-x=-6$$

Subtract 2y from both sides.

$$4xy-x=-6-2y$$

Combine all terms containing x.

$$\left(4y-1\right)x=-6-2y$$

The equation is in standard form.

$$\left(4y-1\right)x=-2y-6$$

Divide both sides by 4y-1.

$$\frac{\left(4y-1\right)x}{4y-1}=\frac{-2y-6}{4y-1}$$

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

$$x=\frac{-2y-6}{4y-1}$$

Divide -6-2y by 4y-1.

$$x=-\frac{2\left(y+3\right)}{4y-1}$$

Solve for y

$$y=-\frac{6-x}{2\left(2x+1\right)}$$

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

Steps for Solving Linear Equation

Combine all terms containing y.

$$\left(4x+2\right)y=x-6$$

Divide both sides by 4x+2.

$$\frac{\left(4x+2\right)y}{4x+2}=\frac{x-6}{4x+2}$$

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

$$y=\frac{x-6}{4x+2}$$

Divide x-6 by 4x+2.

$$y=\frac{x-6}{2\left(2x+1\right)}$$