Solve x*(y+2)*(y-3)=-12

$$x \times (y+2) \times (y-3)=-12$$

Solve for x

$$x=-\frac{12}{\left(y-3\right)\left(y+2\right)}$$

$$y\neq -2\text{ and }y\neq 3$$

Steps for Solving Linear Equation

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

$$\left(xy+2x\right)\left(y-3\right)=-12$$

Use the distributive property to multiply xy+2x by y-3 and combine like terms.

$$xy^{2}-xy-6x=-12$$

Combine all terms containing x.

$$\left(y^{2}-y-6\right)x=-12$$

Divide both sides by y^{2}-y-6.

$$\frac{\left(y^{2}-y-6\right)x}{y^{2}-y-6}=-\frac{12}{y^{2}-y-6}$$

Dividing by y^{2}-y-6 undoes the multiplication by y^{2}-y-6.

$$x=-\frac{12}{y^{2}-y-6}$$

Divide -12 by y^{2}-y-6.

$$x=-\frac{12}{\left(y-3\right)\left(y+2\right)}$$

Solve for y (complex solution)

$$y=\frac{\sqrt{x\left(25x-48\right)}+x}{2x}$$

$$y=\frac{-\sqrt{x\left(25x-48\right)}+x}{2x}\text{, }x\neq 0$$

Solve for y

$$y=\frac{\sqrt{x\left(25x-48\right)}+x}{2x}$$

$$y=\frac{-\sqrt{x\left(25x-48\right)}+x}{2x}\text{, }x<0\text{ or }x\geq \frac{48}{25}$$