Solve {l}{F=mgammav^2}{F+15=mgamma(2w)^2}

$$\left\{ \begin{array} { l } { F = m \gamma v ^ { 2 } } \\ { F + 15 = m \gamma ( 2 w ) ^ { 2 } } \end{array} \right.$$

Solve for F, m, γ, v, w (complex solution)

$$F=m\gamma v^{2}\text{, }m\neq 0\text{, }\gamma \neq 0\text{, }v\in \mathrm{C}\text{, }w=\frac{\sqrt{\frac{m\gamma v^{2}+15}{m\gamma }}}{2}$$

$$F=m\gamma v^{2}\text{, }m\neq 0\text{, }\gamma \neq 0\text{, }v\in \mathrm{C}\text{, }w=-\frac{\sqrt{\frac{m\gamma v^{2}+15}{m\gamma }}}{2}$$

Solve for F, m, γ, v, w

$$\left\{\begin{matrix}\\F=0\text{, }m\neq 0\text{, }\gamma \neq 0\text{, }v=0\text{, }w=-\frac{\sqrt{\frac{15}{m\gamma }}}{2}\text{; }F=m\gamma v^{2}\text{, }m=-\frac{15}{\gamma v^{2}}\text{, }\gamma \neq 0\text{, }v\in \mathrm{R}\text{, }w=-\frac{\sqrt{\frac{m\gamma v^{2}+15}{m\gamma }}}{2}\text{; }F=m\gamma v^{2}\text{, }m>0\text{, }\gamma >0\text{, }v\in \mathrm{R}\text{, }w=-\frac{\sqrt{\frac{m\gamma v^{2}+15}{m\gamma }}}{2}\text{; }F=m\gamma v^{2}\text{, }m<0\text{, }\gamma <0\text{, }v\in \mathrm{R}\text{, }w=-\frac{\sqrt{\frac{m\gamma v^{2}+15}{m\gamma }}}{2}\text{; }F=0\text{, }m\neq 0\text{, }\gamma \neq 0\text{, }v=0\text{, }w=\frac{\sqrt{\frac{15}{m\gamma }}}{2}\text{; }F=m\gamma v^{2}\text{, }m=-\frac{15}{\gamma v^{2}}\text{, }\gamma \neq 0\text{, }v\in \mathrm{R}\text{, }w=\frac{\sqrt{\frac{m\gamma v^{2}+15}{m\gamma }}}{2}\text{; }F=m\gamma v^{2}\text{, }m>0\text{, }\gamma >0\text{, }v\in \mathrm{R}\text{, }w=\frac{\sqrt{\frac{m\gamma v^{2}+15}{m\gamma }}}{2}\text{; }F=m\gamma v^{2}\text{, }m<0\text{, }\gamma <0\text{, }v\in \mathrm{R}\text{, }w=\frac{\sqrt{\frac{m\gamma v^{2}+15}{m\gamma }}}{2}\text{, }&\text{unconditionally}\\F=m\gamma v^{2}\text{, }m\geq -\frac{15}{\gamma v^{2}}\text{, }\gamma \neq 0\text{, }v\in \mathrm{R}\text{, }w=-\frac{\sqrt{\frac{m\gamma v^{2}+15}{m\gamma }}}{2}\text{; }F=m\gamma v^{2}\text{, }m<0\text{, }\gamma \neq 0\text{, }v\in \mathrm{R}\text{, }w=-\frac{\sqrt{\frac{m\gamma v^{2}+15}{m\gamma }}}{2}\text{; }F=m\gamma v^{2}\text{, }m<0\text{, }\gamma >0\text{, }v\in \mathrm{R}\text{, }w=-\frac{\sqrt{\frac{m\gamma v^{2}+15}{m\gamma }}}{2}\text{; }F=m\gamma v^{2}\text{, }m\geq -\frac{15}{\gamma v^{2}}\text{, }\gamma <0\text{, }v\in \mathrm{R}\text{, }w=-\frac{\sqrt{\frac{m\gamma v^{2}+15}{m\gamma }}}{2}\text{; }F=m\gamma v^{2}\text{, }m\geq -\frac{15}{\gamma v^{2}}\text{, }\gamma \neq 0\text{, }v\in \mathrm{R}\text{, }w=\frac{\sqrt{\frac{m\gamma v^{2}+15}{m\gamma }}}{2}\text{; }F=m\gamma v^{2}\text{, }m<0\text{, }\gamma \neq 0\text{, }v\in \mathrm{R}\text{, }w=\frac{\sqrt{\frac{m\gamma v^{2}+15}{m\gamma }}}{2}\text{; }F=m\gamma v^{2}\text{, }m<0\text{, }\gamma >0\text{, }v\in \mathrm{R}\text{, }w=\frac{\sqrt{\frac{m\gamma v^{2}+15}{m\gamma }}}{2}\text{; }F=m\gamma v^{2}\text{, }m\geq -\frac{15}{\gamma v^{2}}\text{, }\gamma <0\text{, }v\in \mathrm{R}\text{, }w=\frac{\sqrt{\frac{m\gamma v^{2}+15}{m\gamma }}}{2}\text{, }&v\neq 0\text{ and }\gamma <0\\F=m\gamma v^{2}\text{, }m>0\text{, }\gamma \neq 0\text{, }v\in \mathrm{R}\text{, }w=-\frac{\sqrt{\frac{m\gamma v^{2}+15}{m\gamma }}}{2}\text{; }F=m\gamma v^{2}\text{, }m\leq -\frac{15}{\gamma v^{2}}\text{, }\gamma \neq 0\text{, }v\in \mathrm{R}\text{, }w=-\frac{\sqrt{\frac{m\gamma v^{2}+15}{m\gamma }}}{2}\text{; }F=m\gamma v^{2}\text{, }m\leq -\frac{15}{\gamma v^{2}}\text{, }\gamma >0\text{, }v\in \mathrm{R}\text{, }w=-\frac{\sqrt{\frac{m\gamma v^{2}+15}{m\gamma }}}{2}\text{; }F=m\gamma v^{2}\text{, }m>0\text{, }\gamma <0\text{, }v\in \mathrm{R}\text{, }w=-\frac{\sqrt{\frac{m\gamma v^{2}+15}{m\gamma }}}{2}\text{; }F=m\gamma v^{2}\text{, }m>0\text{, }\gamma \neq 0\text{, }v\in \mathrm{R}\text{, }w=\frac{\sqrt{\frac{m\gamma v^{2}+15}{m\gamma }}}{2}\text{; }F=m\gamma v^{2}\text{, }m\leq -\frac{15}{\gamma v^{2}}\text{, }\gamma \neq 0\text{, }v\in \mathrm{R}\text{, }w=\frac{\sqrt{\frac{m\gamma v^{2}+15}{m\gamma }}}{2}\text{; }F=m\gamma v^{2}\text{, }m\leq -\frac{15}{\gamma v^{2}}\text{, }\gamma >0\text{, }v\in \mathrm{R}\text{, }w=\frac{\sqrt{\frac{m\gamma v^{2}+15}{m\gamma }}}{2}\text{; }F=m\gamma v^{2}\text{, }m>0\text{, }\gamma <0\text{, }v\in \mathrm{R}\text{, }w=\frac{\sqrt{\frac{m\gamma v^{2}+15}{m\gamma }}}{2}\text{, }&\gamma >0\text{ and }v\neq 0\end{matrix}\right.$$