12x^2+60x^4+24x^6=0

Solution for 12x^2+60x^4+24x^6=0 equation:

Simplifying
12x2 + 60x4 + 24x6 = 0

Solving
12x2 + 60x4 + 24x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12x2'.
12x2(1 + 5x2 + 2x4) = 0

Ignore the factor 12.
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 '(1 + 5x2 + 2x4)' equal to zero and attempt to solve:

Simplifying
1 + 5x2 + 2x4 = 0

Solving
1 + 5x2 + 2x4 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
0.5 + 2.5x2 + x4 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 2.5x2 + -0.5 + x4 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 2.5x2 + x4 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 2.5x2 + x4 = 0 + -0.5
2.5x2 + x4 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
2.5x2 + x4 = -0.5

The x term is 2.5x2.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x2 + 1.5625 + x4 = -0.5 + 1.5625

Reorder the terms:
1.5625 + 2.5x2 + x4 = -0.5 + 1.5625

Combine like terms: -0.5 + 1.5625 = 1.0625
1.5625 + 2.5x2 + x4 = 1.0625

Factor a perfect square on the left side:
(x2 + 1.25)(x2 + 1.25) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(x2 + 1.25) equal to 1.030776406 and -1.030776406.

Subproblem 1
x2 + 1.25 = 1.030776406

Simplifying
x2 + 1.25 = 1.030776406

Reorder the terms:
1.25 + x2 = 1.030776406

Solving
1.25 + x2 = 1.030776406

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x2 = 1.030776406 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x2 = 1.030776406 + -1.25
x2 = 1.030776406 + -1.25

Combine like terms: 1.030776406 + -1.25 = -0.219223594
x2 = -0.219223594

Simplifying
x2 = -0.219223594

Reorder the terms:
0.219223594 + x2 = -0.219223594 + 0.219223594

Combine like terms: -0.219223594 + 0.219223594 = 0.000000000
0.219223594 + x2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

Subproblem 2
x2 + 1.25 = -1.030776406

Simplifying
x2 + 1.25 = -1.030776406

Reorder the terms:
1.25 + x2 = -1.030776406

Solving
1.25 + x2 = -1.030776406

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x2 = -1.030776406 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x2 = -1.030776406 + -1.25
x2 = -1.030776406 + -1.25

Combine like terms: -1.030776406 + -1.25 = -2.280776406
x2 = -2.280776406

Simplifying
x2 = -2.280776406

Reorder the terms:
2.280776406 + x2 = -2.280776406 + 2.280776406

Combine like terms: -2.280776406 + 2.280776406 = 0.000000000
2.280776406 + x2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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