Solve (a+2)^2=(c-b)(c+b+2)

$$( a + 2 ) ^ { 2 } = ( c - b ) ( c + b + 2 )$$

Solve for a (complex solution)

$$a=-\left(\sqrt{c-b}\sqrt{b+c+2}+2\right)$$

$$a=\sqrt{c-b}\sqrt{b+c+2}-2$$

Solve for b (complex solution)

$$b=\sqrt{-\left(a-c+1\right)\left(a+c+3\right)}-1$$

$$b=-\sqrt{-\left(a-c+1\right)\left(a+c+3\right)}-1$$

Solve for a

$$a=-\left(\sqrt{\left(c-b\right)\left(b+c+2\right)}+2\right)$$

$$a=-\left(-\sqrt{\left(c-b\right)\left(b+c+2\right)}+2\right)\text{, }\left(c=-\left(b+2\right)\text{ and }b\geq -1\right)\text{ or }\left(c\leq -\left(b+2\right)\text{ and }c\leq b\text{ and }c\leq -\sqrt{b\left(b+2\right)+1}-1\right)\text{ or }\left(c\geq b\text{ and }c\geq -\left(b+2\right)\text{ and }c\leq -\sqrt{b\left(b+2\right)+1}-1\right)\text{ or }\left(c=b\text{ and }b\leq -1\right)\text{ or }\left(c=-\left(b+2\right)\text{ and }b\leq -1\right)\text{ or }\left(c\leq -\left(b+2\right)\text{ and }c\leq b\text{ and }c\geq \sqrt{b\left(b+2\right)+1}-1\right)\text{ or }\left(c\geq b\text{ and }c\geq -\left(b+2\right)\text{ and }c\geq \sqrt{b\left(b+2\right)+1}-1\right)\text{ or }\left(c=b\text{ and }b\geq -1\right)$$

Solve for b

$$b=\sqrt{-\left(a-c+1\right)\left(a+c+3\right)}-1$$

$$b=-\sqrt{-\left(a-c+1\right)\left(a+c+3\right)}-1\text{, }a=-2\text{ or }\left(c\neq -1\text{ and }a\leq \sqrt{c^{2}+2c+1}-2\text{ and }a\geq -\sqrt{c^{2}+2c+1}-2\right)$$