Solve 9x^2+4x^2+z^2+30y+8z+48=12x-2

$$9 x ^ { 2 } + 4 x ^ { 2 } + z ^ { 2 } + 30 y + 8 z + 48 = 12 x - 2$$

Solve for y

$$y=-\frac{13x^{2}}{30}-\frac{z^{2}}{30}+\frac{2x}{5}-\frac{4z}{15}-\frac{5}{3}$$

Steps for Solving Linear Equation

Combine 9x^{2} and 4x^{2} to get 13x^{2}.

$$13x^{2}+z^{2}+30y+8z+48=12x-2$$

Subtract 13x^{2} from both sides.

$$z^{2}+30y+8z+48=12x-2-13x^{2}$$

Subtract z^{2} from both sides.

$$30y+8z+48=12x-2-13x^{2}-z^{2}$$

Subtract 8z from both sides.

$$30y+48=12x-2-13x^{2}-z^{2}-8z$$

Subtract 48 from both sides.

$$30y=12x-2-13x^{2}-z^{2}-8z-48$$

Subtract 48 from -2 to get -50.

$$30y=12x-50-13x^{2}-z^{2}-8z$$

The equation is in standard form.

$$30y=-13x^{2}+12x-z^{2}-8z-50$$

Divide both sides by 30.

$$\frac{30y}{30}=\frac{-13x^{2}+12x-z^{2}-8z-50}{30}$$

Dividing by 30 undoes the multiplication by 30.

$$y=\frac{-13x^{2}+12x-z^{2}-8z-50}{30}$$

Divide 12x-50-13x^{2}-z^{2}-8z by 30.

$$y=-\frac{13x^{2}}{30}-\frac{z^{2}}{30}+\frac{2x}{5}-\frac{4z}{15}-\frac{5}{3}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{-390y-13z^{2}-104z-614}+6}{13}$$

$$x=\frac{-\sqrt{-390y-13z^{2}-104z-614}+6}{13}$$

Solve for x

$$x=\frac{\sqrt{-390y-13z^{2}-104z-614}+6}{13}$$

$$x=\frac{-\sqrt{-390y-13z^{2}-104z-614}+6}{13}\text{, }y\leq -\frac{z^{2}}{30}-\frac{4z}{15}-\frac{307}{195}$$