x^6+6x^4+12x^2=0

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Solution for x^6+6x^4+12x^2=0 equation: 


Simplifying
x6 + 6x4 + 12x2 = 0

Reorder the terms:
12x2 + 6x4 + x6 = 0

Solving
12x2 + 6x4 + x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(12 + 6x2 + x4) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

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

Subproblem 2
Set the factor '(12 + 6x2 + x4)' equal to zero and attempt to solve:

Simplifying
12 + 6x2 + x4 = 0

Solving
12 + 6x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + 6x2 + -12 + x4 = 0 + -12

Reorder the terms:
12 + -12 + 6x2 + x4 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 6x2 + x4 = 0 + -12
6x2 + x4 = 0 + -12

Combine like terms: 0 + -12 = -12
6x2 + x4 = -12

The x term is 6x2.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x2 + 9 + x4 = -12 + 9

Reorder the terms:
9 + 6x2 + x4 = -12 + 9

Combine like terms: -12 + 9 = -3
9 + 6x2 + x4 = -3

Factor a perfect square on the left side:
(x2 + 3)(x2 + 3) = -3

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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