Solve x^2y+4xy=4

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

Solve for y

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

$$x\neq -4\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Combine all terms containing y.

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

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

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

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

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

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

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

Solve for x (complex solution)

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

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

Solve for x

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

$$x=-\frac{2\sqrt{y^{2}+y}}{y}-2\text{, }y>0\text{ or }y\leq -1$$