Solve -2*x*(-3)+3^2+y^2-2*y*2+z^2=4

$$- 2 \cdot x \cdot ( - 3 ) + 3 ^ { 2 } + y ^ { 2 } - 2 \cdot y \cdot 2 + z ^ { 2 } = 4$$

Solve for x

$$x=-\frac{y^{2}}{6}-\frac{z^{2}}{6}+\frac{2y}{3}-\frac{5}{6}$$

Steps for Solving Linear Equation

Multiply -2 and -3 to get 6.

$$6x+3^{2}+y^{2}-2y\times 2+z^{2}=4$$

Calculate 3 to the power of 2 and get 9.

$$6x+9+y^{2}-2y\times 2+z^{2}=4$$

Multiply 2 and 2 to get 4.

$$6x+9+y^{2}-4y+z^{2}=4$$

Subtract 9 from both sides.

$$6x+y^{2}-4y+z^{2}=4-9$$

Subtract 9 from 4 to get -5.

$$6x+y^{2}-4y+z^{2}=-5$$

Subtract y^{2} from both sides.

$$6x-4y+z^{2}=-5-y^{2}$$

Add 4y to both sides.

$$6x+z^{2}=-5-y^{2}+4y$$

Subtract z^{2} from both sides.

$$6x=-5-y^{2}+4y-z^{2}$$

The equation is in standard form.

$$6x=-y^{2}+4y-z^{2}-5$$

Divide both sides by 6.

$$\frac{6x}{6}=\frac{-y^{2}+4y-z^{2}-5}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$x=\frac{-y^{2}+4y-z^{2}-5}{6}$$

Divide -5-y^{2}+4y-z^{2} by 6.

$$x=-\frac{y^{2}}{6}-\frac{z^{2}}{6}+\frac{2y}{3}-\frac{5}{6}$$

Solve for y

$$y=\sqrt{-6x-z^{2}-1}+2$$

$$y=-\sqrt{-6x-z^{2}-1}+2\text{, }x\leq \frac{-z^{2}-1}{6}$$