Solve y^2+6x-6y+21=0

$$y ^ { 2 } + 6 x - 6 y + 21 = 0$$

Solve for x

$$x=-\frac{y^{2}}{6}+y-\frac{7}{2}$$

Steps for Solving Linear Equation

Subtract y^{2} from both sides. Anything subtracted from zero gives its negation.

$$6x-6y+21=-y^{2}$$

Add 6y to both sides.

$$6x+21=-y^{2}+6y$$

Subtract 21 from both sides.

$$6x=-y^{2}+6y-21$$

Divide both sides by 6.

$$\frac{6x}{6}=\frac{-y^{2}+6y-21}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$x=\frac{-y^{2}+6y-21}{6}$$

Divide -y^{2}+6y-21 by 6.

$$x=-\frac{y^{2}}{6}+y-\frac{7}{2}$$

Solve for y (complex solution)

$$y=\sqrt{-6x-12}+3$$

$$y=-\sqrt{-6x-12}+3$$

Solve for y

$$y=\sqrt{-6x-12}+3$$

$$y=-\sqrt{-6x-12}+3\text{, }x\leq -2$$