Solve 4x+y+2xy+1=0

$$4 x + y + 2 x y + 1 = 0$$

Solve for x

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

$$y\neq -2$$

Steps for Solving Linear Equation

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

$$4x+2xy+1=-y$$

Subtract 1 from both sides.

$$4x+2xy=-y-1$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 4+2y.

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

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

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

Divide -y-1 by 4+2y.

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

Solve for y

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

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

Steps for Solving Linear Equation

Subtract 4x from both sides. Anything subtracted from zero gives its negation.

$$y+2xy+1=-4x$$

Subtract 1 from both sides.

$$y+2xy=-4x-1$$

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by 1+2x.

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

Dividing by 1+2x undoes the multiplication by 1+2x.

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

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

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