Solve F=mV^2/r

$$F = \frac { m V ^ { 2 } } { r }$$

Solve for V (complex solution)

$$\left\{\begin{matrix}V=-m^{-\frac{1}{2}}\sqrt{F}\sqrt{r}\text{; }V=m^{-\frac{1}{2}}\sqrt{F}\sqrt{r}\text{, }&m\neq 0\text{ and }r\neq 0\\V\in \mathrm{C}\text{, }&F=0\text{ and }m=0\text{ and }r\neq 0\end{matrix}\right.$$

Solve for F

$$F=\frac{mV^{2}}{r}$$

$$r\neq 0$$

Solve for V

$$\left\{\begin{matrix}V=\sqrt{\frac{Fr}{m}}\text{; }V=-\sqrt{\frac{Fr}{m}}\text{, }&\left(F\geq 0\text{ and }m<0\text{ and }r<0\right)\text{ or }\left(F\leq 0\text{ and }m>0\text{ and }r<0\right)\text{ or }\left(F\geq 0\text{ and }m>0\text{ and }r>0\right)\text{ or }\left(F\leq 0\text{ and }m<0\text{ and }r>0\right)\\V\in \mathrm{R}\text{, }&F=0\text{ and }m=0\text{ and }r\neq 0\end{matrix}\right.$$