Solve 2x(x-y)=3x-9

$$2 x ( x - y ) = 3 x - 9$$

Solve for y

$$y=x-\frac{3}{2}+\frac{9}{2x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$2x^{2}-2xy=3x-9$$

Subtract 2x^{2} from both sides.

$$-2xy=3x-9-2x^{2}$$

The equation is in standard form.

$$\left(-2x\right)y=-2x^{2}+3x-9$$

Divide both sides by -2x.

$$\frac{\left(-2x\right)y}{-2x}=\frac{-2x^{2}+3x-9}{-2x}$$

Dividing by -2x undoes the multiplication by -2x.

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

Divide 3x-9-2x^{2} by -2x.

$$y=x-\frac{3}{2}+\frac{9}{2x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{4y^{2}+12y-63}}{4}+\frac{y}{2}+\frac{3}{4}$$

$$x=-\frac{\sqrt{4y^{2}+12y-63}}{4}+\frac{y}{2}+\frac{3}{4}$$

Solve for x

$$x=\frac{\sqrt{4y^{2}+12y-63}}{4}+\frac{y}{2}+\frac{3}{4}$$

$$x=-\frac{\sqrt{4y^{2}+12y-63}}{4}+\frac{y}{2}+\frac{3}{4}\text{, }y\geq 3\sqrt{2}-\frac{3}{2}\text{ or }y\leq -3\sqrt{2}-\frac{3}{2}$$