3a^4+2a^2-96=0

Solution for 3a^4+2a^2-96=0 equation:

Simplifying
3a4 + 2a2 + -96 = 0

Reorder the terms:
-96 + 2a2 + 3a4 = 0

Solving
-96 + 2a2 + 3a4 = 0

Solving for variable 'a'.

Factor a trinomial.
(-6 + -1a2)(16 + -3a2) = 0

Subproblem 1
Set the factor '(-6 + -1a2)' equal to zero and attempt to solve:

Simplifying
-6 + -1a2 = 0

Solving
-6 + -1a2 = 0

Move all terms containing a to the left, all other terms to the right.

Add '6' to each side of the equation.
-6 + 6 + -1a2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1a2 = 0 + 6
-1a2 = 0 + 6

Combine like terms: 0 + 6 = 6
-1a2 = 6

Divide each side by '-1'.
a2 = -6

Simplifying
a2 = -6

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(16 + -3a2)' equal to zero and attempt to solve:

Simplifying
16 + -3a2 = 0

Solving
16 + -3a2 = 0

Move all terms containing a to the left, all other terms to the right.

Add '-16' to each side of the equation.
16 + -16 + -3a2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -3a2 = 0 + -16
-3a2 = 0 + -16

Combine like terms: 0 + -16 = -16
-3a2 = -16

Divide each side by '-3'.
a2 = 5.333333333

Simplifying
a2 = 5.333333333

Take the square root of each side:
a = {-2.309401077, 2.309401077}
Solution
a = {-2.309401077, 2.309401077}