Solve -4x+12/x=4x+y

$$-4x+ \frac{ 12 }{ x } =4x+y$$

Solve for y

$$y=-8x+\frac{12}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$-4xx+12=4xx+xy$$

Multiply x and x to get x^{2}.

$$-4x^{2}+12=4xx+xy$$

Multiply x and x to get x^{2}.

$$-4x^{2}+12=4x^{2}+xy$$

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

$$4x^{2}+xy=-4x^{2}+12$$

Subtract 4x^{2} from both sides.

$$xy=-4x^{2}+12-4x^{2}$$

Combine -4x^{2} and -4x^{2} to get -8x^{2}.

$$xy=-8x^{2}+12$$

The equation is in standard form.

$$xy=12-8x^{2}$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{12-8x^{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$y=\frac{12-8x^{2}}{x}$$

Divide 12-8x^{2} by x.

$$y=-8x+\frac{12}{x}$$

Solve for x

$$x=\frac{-\sqrt{y^{2}+384}-y}{16}$$

$$x=\frac{\sqrt{y^{2}+384}-y}{16}$$