Solve x+x*y+x*y^2=2

$$x+x \times y+x \times { y }^{ 2 } =2$$

Solve for x (complex solution)

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

$$y\neq \frac{-1+\sqrt{3}i}{2}\text{ and }y\neq \frac{-\sqrt{3}i-1}{2}$$

Steps for Solving Linear Equation

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 1+y+y^{2}.

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

Dividing by 1+y+y^{2} undoes the multiplication by 1+y+y^{2}.

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

Solve for x

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

Steps for Solving Linear Equation

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 1+y+y^{2}.

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

Dividing by 1+y+y^{2} undoes the multiplication by 1+y+y^{2}.

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

Solve for y (complex solution)

$$y=\frac{\sqrt{8x-3x^{2}}}{2x}-\frac{1}{2}$$

$$y=-\frac{\sqrt{8x-3x^{2}}}{2x}-\frac{1}{2}\text{, }x\neq 0$$

Solve for y

$$y=\frac{\sqrt{-3+\frac{8}{x}}-1}{2}$$

$$y=\frac{-\sqrt{-3+\frac{8}{x}}-1}{2}\text{, }x>0\text{ and }x\leq \frac{8}{3}$$