3a^6+12a^4-96a^2=0

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Solution for 3a^6+12a^4-96a^2=0 equation: 


Simplifying
3a6 + 12a4 + -96a2 = 0

Reorder the terms:
-96a2 + 12a4 + 3a6 = 0

Solving
-96a2 + 12a4 + 3a6 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3a2'.
3a2(-32 + 4a2 + a4) = 0

Factor a trinomial.
3a2((-8 + -1a2)(4 + -1a2)) = 0

Factor a difference between two squares.
3a2((-8 + -1a2)((2 + a)(2 + -1a))) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'a2' equal to zero and attempt to solve:

Simplifying
a2 = 0

Solving
a2 = 0

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

Simplifying
a2 = 0

Take the square root of each side:
a = {0}

Subproblem 2
Set the factor '(-8 + -1a2)' equal to zero and attempt to solve:

Simplifying
-8 + -1a2 = 0

Solving
-8 + -1a2 = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1a2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1a2 = 0 + 8
-1a2 = 0 + 8

Combine like terms: 0 + 8 = 8
-1a2 = 8

Divide each side by '-1'.
a2 = -8

Simplifying
a2 = -8

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
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 4
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 = {0, -2, 2}

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