12x^4+4Ax^2-A^2=0

Solution for 12x^4+4Ax^2-A^2=0 equation:

Simplifying
12x4 + 4Ax2 + -1A2 = 0

Reorder the terms:
-1A2 + 4x2A + 12x4 = 0

Solving
-1A2 + 4x2A + 12x4 = 0

Solving for variable 'A'.

Factor a trinomial.
(-1A + -2x2)(A + -6x2) = 0

Subproblem 1
Set the factor '(-1A + -2x2)' equal to zero and attempt to solve:

Simplifying
-1A + -2x2 = 0

Solving
-1A + -2x2 = 0

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

Add '2x2' to each side of the equation.
-1A + -2x2 + 2x2 = 0 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-1A + 0 = 0 + 2x2
-1A = 0 + 2x2
Remove the zero:
-1A = 2x2

Divide each side by '-1'.
A = -2x2

Simplifying
A = -2x2
Subproblem 2
Set the factor '(A + -6x2)' equal to zero and attempt to solve:

Simplifying
A + -6x2 = 0

Solving
A + -6x2 = 0

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

Add '6x2' to each side of the equation.
A + -6x2 + 6x2 = 0 + 6x2

Combine like terms: -6x2 + 6x2 = 0
A + 0 = 0 + 6x2
A = 0 + 6x2
Remove the zero:
A = 6x2

Simplifying
A = 6x2
Solution
A = {-2x2, 6x2}