Solve xy^2+2y=4

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

Solve for x

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

$$y\neq 0$$

Steps for Solving Linear Equation

Subtract 2y from both sides.

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

The equation is in standard form.

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

Divide both sides by y^{2}.

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

Dividing by y^{2} undoes the multiplication by y^{2}.

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

Divide 4-2y by y^{2}.

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

Solve for y (complex solution)

$$\left\{\begin{matrix}y=\frac{\sqrt{4x+1}-1}{x}\text{; }y=-\frac{\sqrt{4x+1}+1}{x}\text{, }&x\neq 0\\y=2\text{, }&x=0\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}y=\frac{\sqrt{4x+1}-1}{x}\text{; }y=-\frac{\sqrt{4x+1}+1}{x}\text{, }&x\neq 0\text{ and }x\geq -\frac{1}{4}\\y=2\text{, }&x=0\end{matrix}\right.$$