Solve xy-x+2y^2=2

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

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=-2y-2\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 2y^{2} from both sides.

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

Combine all terms containing x.

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

Divide both sides by -1+y.

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

Dividing by -1+y undoes the multiplication by -1+y.

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

Divide -2y^{2}+2 by -1+y.

$$x=-2y-2$$

Solve for x

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

Steps for Solving Linear Equation

Subtract 2y^{2} from both sides.

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

Combine all terms containing x.

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

Divide both sides by -1+y.

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

Dividing by -1+y undoes the multiplication by -1+y.

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

Divide -2y^{2}+2 by -1+y.

$$x=-2y-2$$

Solve for y

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

$$y=1$$