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

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

Simplifying
2x6 + 60x2 + 2x4 = 0

Reorder the terms:
60x2 + 2x4 + 2x6 = 0

Solving
60x2 + 2x4 + 2x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(30 + x2 + x4) = 0

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

Simplifying
30 + x2 + x4 = 0

Solving
30 + x2 + x4 = 0

Begin completing the square.

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + x2 + -30 + x4 = 0 + -30

Reorder the terms:
30 + -30 + x2 + x4 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + x2 + x4 = 0 + -30
x2 + x4 = 0 + -30

Combine like terms: 0 + -30 = -30
x2 + x4 = -30

The x term is x2.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x2 + 0.25 + x4 = -30 + 0.25

Reorder the terms:
0.25 + x2 + x4 = -30 + 0.25

Combine like terms: -30 + 0.25 = -29.75
0.25 + x2 + x4 = -29.75

Factor a perfect square on the left side:
(x2 + 0.5)(x2 + 0.5) = -29.75

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}