Question 57
Find all values of the real parameter $a$ such that the number of the solutions of the equation
$$
3\left(5 x^{2}-a^{4}\right)-2 x=2 a^{2}(6 x-1)
$$
does not exceed the number of the solutions of the equation
$$
2 x^{3}+6 x=\left(3^{6 a}-9\right) \sqrt{2^{8 a}-\frac{1}{6}}-(3 a-1)^{2} 12^{x}
$$
$$
3\left(5 x^{2}-a^{4}\right)-2 x=2 a^{2}(6 x-1)
$$
does not exceed the number of the solutions of the equation
$$
2 x^{3}+6 x=\left(3^{6 a}-9\right) \sqrt{2^{8 a}-\frac{1}{6}}-(3 a-1)^{2} 12^{x}
$$