Solve x^2y+3xy+3=0

$${ x }^{ 2 } y+3xy+3=0$$

Solve for y

$$y=-\frac{3}{x\left(x+3\right)}$$

$$x\neq -3\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}y+3xy=-3$$

Combine all terms containing y.

$$\left(x^{2}+3x\right)y=-3$$

Divide both sides by x^{2}+3x.

$$\frac{\left(x^{2}+3x\right)y}{x^{2}+3x}=-\frac{3}{x^{2}+3x}$$

Dividing by x^{2}+3x undoes the multiplication by x^{2}+3x.

$$y=-\frac{3}{x^{2}+3x}$$

Divide -3 by x^{2}+3x.

$$y=-\frac{3}{x\left(x+3\right)}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{9y^{2}-12y}}{2y}-\frac{3}{2}$$

$$x=-\frac{\sqrt{9y^{2}-12y}}{2y}-\frac{3}{2}\text{, }y\neq 0$$

Solve for x

$$x=\frac{\sqrt{9y^{2}-12y}}{2y}-\frac{3}{2}$$

$$x=-\frac{\sqrt{9y^{2}-12y}}{2y}-\frac{3}{2}\text{, }y<0\text{ or }y\geq \frac{4}{3}$$