The answer is a = 3/4 = 0.75
First get rid of the paranthesis,
[tex] {a}^{2} (64 {a}^{2} - 3) = 64 {a}^{4} - 3 {a}^{2} [/tex]
Then set the denominators equal:
[tex] \frac{ 256 {a}^{4} - 12 {a}^{2}}{12} = \frac{81 - 12 {a}^{2} }{12} [/tex]
Then remove the denominators and solve:
[tex]256 {a}^{4} - 12 {a}^{2} = 81 - 12 {a}^{2} [/tex]
Eliminate -12a^2 by adding 12a^2 to both sides:
[tex]256 {a}^{4} = 81[/tex]
Take the fourth root of them or take the square root twice:
[tex] \sqrt[4]{256 {a}^{4} } = \sqrt[4]{81} \\ 4a = 3[/tex]
Divide both sides by 4:
[tex]a = \frac{3}{4} = 0.75[/tex]
