Solve x^2y=4xy-6

$$x ^ { 2 } y = 4 x y - 6$$

Solve for y

$$y=-\frac{6}{x\left(x-4\right)}$$

$$x\neq 4\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Subtract 4xy from both sides.

$$x^{2}y-4xy=-6$$

Combine all terms containing y.

$$\left(x^{2}-4x\right)y=-6$$

Divide both sides by x^{2}-4x.

$$\frac{\left(x^{2}-4x\right)y}{x^{2}-4x}=-\frac{6}{x^{2}-4x}$$

Dividing by x^{2}-4x undoes the multiplication by x^{2}-4x.

$$y=-\frac{6}{x^{2}-4x}$$

Divide -6 by x^{2}-4x.

$$y=-\frac{6}{x\left(x-4\right)}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{4y^{2}-6y}}{y}+2$$

$$x=-\frac{\sqrt{4y^{2}-6y}}{y}+2\text{, }y\neq 0$$

Solve for x

$$x=\frac{\sqrt{4y^{2}-6y}}{y}+2$$

$$x=-\frac{\sqrt{4y^{2}-6y}}{y}+2\text{, }y<0\text{ or }y\geq \frac{3}{2}$$