Solve {frac{(sqrt{12-x^{2}}-y)((x+4)^{2}+(y+4)^2-8(x+4)+x^2-y^2-24)}{2-x^2}=0

$$\{ \frac { ( \sqrt { 12 - x ^ { 2 } } - y ) ( ( x + 4 ) ^ { 2 } + ( y + 4 ) ^ { 2 } - 8 ( x + 4 ) + x ^ { 2 } - y ^ { 2 } - 24 ) } { 2 - x ^ { 2 } } = 0$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\sqrt{12-y^{2}}\text{; }x=\sqrt{12-y^{2}}\text{, }&y\neq \sqrt{10}\text{ and }\left(y=0\text{ or }arg(y)<\pi \right)\text{ and }y\neq -\sqrt{10}\\x=-2\sqrt{3-y}\text{; }x=2\sqrt{3-y}\text{, }&y\neq \frac{5}{2}\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\sqrt{12-y^{2}}\text{; }x=-\sqrt{12-y^{2}}\text{, }&y\neq \sqrt{10}\text{ and }y\leq 2\sqrt{3}\text{ and }y\geq 0\\x=2\sqrt{3-y}\text{; }x=-2\sqrt{3-y}\text{, }&y\geq 0\text{ and }y\neq \frac{5}{2}\text{ and }y\leq 3\end{matrix}\right.$$