3a^4-9a^2-12=0

Solution for 3a^4-9a^2-12=0 equation:

Simplifying
3a4 + -9a2 + -12 = 0

Reorder the terms:
-12 + -9a2 + 3a4 = 0

Solving
-12 + -9a2 + 3a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + -3a2 + a4) = 0

Factor a trinomial.
3((-1 + -1a2)(4 + -1a2)) = 0

Factor a difference between two squares.
3((-1 + -1a2)((2 + a)(2 + -1a))) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -1a2)' equal to zero and attempt to solve:

Simplifying
-1 + -1a2 = 0

Solving
-1 + -1a2 = 0

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

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

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

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

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

Simplifying
a2 = -1

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 '(2 + a)' equal to zero and attempt to solve:

Simplifying
2 + a = 0

Solving
2 + a = 0

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

Add '-2' to each side of the equation.
2 + -2 + a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + a = 0 + -2
a = 0 + -2

Combine like terms: 0 + -2 = -2
a = -2

Simplifying
a = -2
Subproblem 3
Set the factor '(2 + -1a)' equal to zero and attempt to solve:

Simplifying
2 + -1a = 0

Solving
2 + -1a = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {-2, 2}