0=2x^6+10x^4-12x^2

Solution for 0=2x^6+10x^4-12x^2 equation:

Simplifying
0 = 2x6 + 10x4 + -12x2

Reorder the terms:
0 = -12x2 + 10x4 + 2x6

Solving
0 = -12x2 + 10x4 + 2x6

Solving for variable 'x'.
Remove the zero:
12x2 + -10x4 + -2x6 = -12x2 + 10x4 + 2x6 + 12x2 + -10x4 + -2x6

Reorder the terms:
12x2 + -10x4 + -2x6 = -12x2 + 12x2 + 10x4 + -10x4 + 2x6 + -2x6

Combine like terms: -12x2 + 12x2 = 0
12x2 + -10x4 + -2x6 = 0 + 10x4 + -10x4 + 2x6 + -2x6
12x2 + -10x4 + -2x6 = 10x4 + -10x4 + 2x6 + -2x6

Combine like terms: 10x4 + -10x4 = 0
12x2 + -10x4 + -2x6 = 0 + 2x6 + -2x6
12x2 + -10x4 + -2x6 = 2x6 + -2x6

Combine like terms: 2x6 + -2x6 = 0
12x2 + -10x4 + -2x6 = 0

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(6 + -5x2 + -1x4) = 0

Factor a trinomial.
2x2((1 + -1x2)(6 + x2)) = 0

Factor a difference between two squares.
2x2(((1 + x)(1 + -1x))(6 + x2)) = 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 '(6 + x2)' equal to zero and attempt to solve:

Simplifying
6 + x2 = 0

Solving
6 + x2 = 0

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

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

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

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

Simplifying
x2 = -6

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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Subproblem 4
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {0, -1, 1}