a^4-a^2b^2-12b^4=0

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


Simplifying
a4 + -1a2b2 + -12b4 = 0

Reorder the terms:
-1a2b2 + a4 + -12b4 = 0

Solving
-1a2b2 + a4 + -12b4 = 0

Solving for variable 'a'.

Factor a trinomial.
(a2 + -4b2)(a2 + 3b2) = 0

Factor a difference between two squares.
((a + 2b)(a + -2b))(a2 + 3b2) = 0


Subproblem 1
Set the factor '(a2 + 3b2)' equal to zero and attempt to solve:

Simplifying
a2 + 3b2 = 0

Solving
a2 + 3b2 = 0

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

Add '-3b2' to each side of the equation.
a2 + 3b2 + -3b2 = 0 + -3b2

Combine like terms: 3b2 + -3b2 = 0
a2 + 0 = 0 + -3b2
a2 = 0 + -3b2
Remove the zero:
a2 = -3b2

Simplifying
a2 = -3b2

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

Simplifying
a + 2b = 0

Solving
a + 2b = 0

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

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

Combine like terms: 2b + -2b = 0
a + 0 = 0 + -2b
a = 0 + -2b
Remove the zero:
a = -2b

Simplifying
a = -2b

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

Simplifying
a + -2b = 0

Solving
a + -2b = 0

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

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

Combine like terms: -2b + 2b = 0
a + 0 = 0 + 2b
a = 0 + 2b
Remove the zero:
a = 2b

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

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