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

$${ x }^{ 2 } y+4xy+4 = -4y$$

Solve for y

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

$$x\neq -2$$

Steps for Solving Linear Equation

Add 4y to both sides.

$$x^{2}y+4xy+4+4y=0$$

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

$$x^{2}y+4xy+4y=-4$$

Combine all terms containing y.

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

Divide both sides by x^{2}+4x+4.

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

Dividing by x^{2}+4x+4 undoes the multiplication by x^{2}+4x+4.

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

Divide -4 by x^{2}+4x+4.

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

Solve for x (complex solution)

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

$$x=-2-\frac{2\sqrt{-y}}{y}\text{, }y\neq 0$$

Solve for x

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

$$x=-2-\frac{2\sqrt{-y}}{y}\text{, }y<0$$