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

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

Solve for x (complex solution)

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

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

Solve for y (complex solution)

$$y=-\left(\sqrt{-x^{2}+6x-z^{2}-5}+2\right)$$

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

Solve for x

$$\left\{\begin{matrix}x=-\sqrt{4-z^{2}}+3\text{; }x=\sqrt{4-z^{2}}+3\text{, }&y=-2\text{ and }|z|\leq 2\\x=-\sqrt{-y^{2}-4y-z^{2}}+3\text{; }x=\sqrt{-y^{2}-4y-z^{2}}+3\text{, }&\left(y=-2\text{ or }z>-2\right)\text{ and }y\leq \sqrt{4-z^{2}}-2\text{ and }y\geq -\sqrt{4-z^{2}}-2\text{ and }|z|<2\end{matrix}\right.$$

Solve for y

$$\left\{\begin{matrix}y=-\sqrt{4-z^{2}}-2\text{; }y=\sqrt{4-z^{2}}-2\text{, }&x=3\text{ and }|z|\leq 2\\y=-\left(\sqrt{-x^{2}+6x-z^{2}-5}+2\right)\text{; }y=\sqrt{-x^{2}+6x-z^{2}-5}-2\text{, }&\left(x=3\text{ or }z>-2\right)\text{ and }x\leq \sqrt{4-z^{2}}+3\text{ and }x\geq -\sqrt{4-z^{2}}+3\text{ and }|z|<2\end{matrix}\right.$$