Solve 9m^2-6am+2a^2-2c^2/9m^2-6am=3m-4a/3m-2a

$$\frac { 9 m ^ { 2 } - 6 a m + 2 a ^ { 2 } - 2 c ^ { 2 } } { 9 m ^ { 2 } - 6 a m } = \frac { 3 m - 4 a } { 3 m - 2 a }$$

Solve for a

$$\left\{\begin{matrix}a=\frac{-\sqrt{9m^{2}+4c^{2}}-3m}{2}\text{, }&\left(c>0\text{ and }m\neq -\frac{2\sqrt{3}c}{9}\text{ and }m\neq 0\right)\text{ or }\left(m\neq \frac{2\sqrt{3}c}{9}\text{ and }c<0\text{ and }m\neq 0\right)\text{ or }\left(m\neq 0\text{ and }|m|\neq \frac{2\sqrt{3}|c|}{9}\right)\\a=\frac{\sqrt{9m^{2}+4c^{2}}-3m}{2}\text{, }&\left(c<0\text{ and }m\neq -\frac{2\sqrt{3}c}{9}\text{ and }m\neq 0\right)\text{ or }\left(m\neq \frac{2\sqrt{3}c}{9}\text{ and }c>0\text{ and }m\neq 0\right)\text{ or }\left(m\neq 0\text{ and }|m|\neq \frac{2\sqrt{3}|c|}{9}\right)\end{matrix}\right.$$

Solve for c

$$c=\sqrt{a\left(3m+a\right)}$$

$$c=-\sqrt{a\left(3m+a\right)}\text{, }\left(a\leq 0\text{ or }m\geq -\frac{a}{3}\right)\text{ and }\left(a\geq 0\text{ or }m\leq -\frac{a}{3}\right)\text{ and }m\neq 0\text{ and }m\neq \frac{2a}{3}$$