Solve (am^2-1am-2)^2-a(m^2+1)(2m-a)(2m-5)=0

$$( a m ^ { 2 } - 1 a m - 2 ) ^ { 2 } - a ( m ^ { 2 } + 1 ) ( 2 m - a ) ( 2 m - 5 ) = 0$$

Solve for a

$$\left\{\begin{matrix}a=\frac{\sqrt{\left(2m-5\right)\left(m^{2}+1\right)\left(2m^{5}-5m^{4}+6m^{3}-9m^{2}-4\right)}+2m^{4}-5m^{3}+4m^{2}-7m}{m^{4}-4m^{2}+2m-5}\text{; }a=\frac{-\sqrt{\left(2m-5\right)\left(m^{2}+1\right)\left(2m^{5}-5m^{4}+6m^{3}-9m^{2}-4\right)}+2m^{4}-5m^{3}+4m^{2}-7m}{m^{4}-4m^{2}+2m-5}\text{, }&m^{4}-4m^{2}+2m-5\neq 0\text{ and }4m^{8}-20m^{7}+41m^{6}-68m^{5}+82m^{4}-56m^{3}+65m^{2}-8m+20\geq 0\\a=-\frac{2}{m\left(7-4m+5m^{2}-2m^{3}\right)}\text{, }&m^{4}-4m^{2}+2m-5=0\text{ and }m\neq \frac{\sqrt[3]{18\sqrt{322}+323}+\sqrt[3]{323-18\sqrt{322}}+5}{6}\text{ and }m\neq 0\end{matrix}\right.$$