Solve M=MO/sqrt{1-frac{V^2{C^2}}}

$$M = \frac { M O } { \sqrt { 1 - \frac { V ^ { 2 } } { C ^ { 2 } } } }$$

Solve for C (complex solution)

$$\left\{\begin{matrix}C=-i\left(O^{2}-1\right)^{-\frac{1}{2}}V\text{; }C=i\left(O^{2}-1\right)^{-\frac{1}{2}}V\text{, }&O\neq 0\text{ and }V\neq 0\text{ and }O\neq 1\text{ and }O\neq -1\text{ and }arg(O)<\pi \\C\neq 0\text{, }&O=1\text{ and }V=0\\C\in \mathrm{C}\setminus V\text{, }V\neq 0,-V\text{, }V\neq 0,0\text{, }&M=0\end{matrix}\right.$$

Solve for M (complex solution)

$$\left\{\begin{matrix}M=0\text{, }&C\neq 0\text{ and }V\neq C\text{ and }V\neq -C\\M\in \mathrm{C}\text{, }&\left(V=-C\sqrt{1-O^{2}}\text{ or }V=C\sqrt{1-O^{2}}\right)\text{ and }C\neq 0\text{ and }arg(O)<\pi \text{ and }O\neq 0\end{matrix}\right.$$

Solve for C

$$\left\{\begin{matrix}C=-\sqrt{-\frac{1}{O^{2}-1}}V\text{, }&\sqrt{O+1}-\sqrt{-\frac{1}{O-1}}<0\text{ and }V\neq 0\text{ and }O<1\text{ and }O>0\\C=\sqrt{-\frac{1}{O^{2}-1}}V\text{, }&-\sqrt{O+1}+\sqrt{-\frac{1}{O-1}}>0\text{ and }V\neq 0\text{ and }O<1\text{ and }O>0\\C\neq 0\text{, }&V=0\text{ and }O=1\\C\in \mathrm{R}\setminus \left(-V\text{, }V\neq 0,V\text{, }V\neq 0,0\cup \begin{bmatrix}-|V|,|V|\end{bmatrix}\right)\text{, }&O\neq 0\text{ and }M=0\\C\in \mathrm{R}\setminus \left(-V\text{, }V\neq 0,V\text{, }V\neq 0,0\cup \left(-|V|,0\right)\text{, }V\neq 0\cup \left(0,|V|\right)\text{, }V\neq 0\right)\text{, }&M=0\text{ and }O=0\end{matrix}\right.$$

Solve for M

$$\left\{\begin{matrix}M=0\text{, }&\left(V<C\text{ and }V>-C\text{ and }C\neq 0\text{ and }|V|<|C|\right)\text{ or }\left(V>C\text{ and }V<-C\text{ and }C\neq 0\text{ and }|V|<|C|\right)\\M\in \mathrm{R}\text{, }&C\neq 0\text{ and }O\leq 1\text{ and }|V|=|C|\sqrt{1-O^{2}}\text{ and }|V|<|C|\text{ and }O>0\end{matrix}\right.$$