Solve x^2-4y-6x-8y=27

$${ x }^{ 2 } -4y-6x-8y=27$$

Solve for y

$$y=\frac{\left(x-9\right)\left(x+3\right)}{12}$$

Steps for Solving Linear Equation

Combine -4y and -8y to get -12y.

$$x^{2}-12y-6x=27$$

Subtract x^{2} from both sides.

$$-12y-6x=27-x^{2}$$

Add 6x to both sides.

$$-12y=27-x^{2}+6x$$

The equation is in standard form.

$$-12y=27+6x-x^{2}$$

Divide both sides by -12.

$$\frac{-12y}{-12}=-\frac{\left(x-9\right)\left(x+3\right)}{-12}$$

Dividing by -12 undoes the multiplication by -12.

$$y=-\frac{\left(x-9\right)\left(x+3\right)}{-12}$$

Divide -\left(-9+x\right)\left(3+x\right) by -12.

$$y=\frac{\left(x-9\right)\left(x+3\right)}{12}$$

Solve for x (complex solution)

$$x=2\sqrt{3y+9}+3$$

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

Solve for x

$$x=2\sqrt{3y+9}+3$$

$$x=-2\sqrt{3y+9}+3\text{, }y\geq -3$$