Solve y=(2+x)y^2

$$y = ( 2 + x ) y ^ { 2 }$$

Solve for x

$$\left\{\begin{matrix}x=-2+\frac{1}{y}\text{, }&y\neq 0\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2+x by y^{2}.

$$y=2y^{2}+xy^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$2y^{2}+xy^{2}=y$$

Subtract 2y^{2} from both sides.

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

The equation is in standard form.

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

Divide both sides by y^{2}.

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

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

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

Divide y\left(1-2y\right) by y^{2}.

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

Solve for y

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