Solve 2019=x(y^2+y+1)

$$2019 = x ( y ^ { 2 } + y + 1 )$$

Solve for x (complex solution)

$$x=\frac{2019}{y^{2}+y+1}$$

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

Steps for Solving Linear Equation

Use the distributive property to multiply x by y^{2}+y+1.

$$2019=xy^{2}+xy+x$$

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

$$xy^{2}+xy+x=2019$$

Combine all terms containing x.

$$\left(y^{2}+y+1\right)x=2019$$

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

$$\frac{\left(y^{2}+y+1\right)x}{y^{2}+y+1}=\frac{2019}{y^{2}+y+1}$$

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

$$x=\frac{2019}{y^{2}+y+1}$$

Solve for x

$$x=\frac{2019}{y^{2}+y+1}$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by y^{2}+y+1.

$$2019=xy^{2}+xy+x$$

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

$$xy^{2}+xy+x=2019$$

Combine all terms containing x.

$$\left(y^{2}+y+1\right)x=2019$$

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

$$\frac{\left(y^{2}+y+1\right)x}{y^{2}+y+1}=\frac{2019}{y^{2}+y+1}$$

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

$$x=\frac{2019}{y^{2}+y+1}$$

Solve for y (complex solution)

$$y=\frac{\sqrt{8076x-3x^{2}}}{2x}-\frac{1}{2}$$

$$y=-\frac{\sqrt{8076x-3x^{2}}}{2x}-\frac{1}{2}\text{, }x\neq 0$$

Solve for y

$$y=\frac{\sqrt{-3+\frac{8076}{x}}-1}{2}$$

$$y=\frac{-\sqrt{-3+\frac{8076}{x}}-1}{2}\text{, }x>0\text{ and }x\leq 2692$$