2x^8=2x^6

Solution for 2x^8=2x^6 equation:

Simplifying
2x8 = 2x6

Solving
2x8 = 2x6

Solving for variable 'x'.

Reorder the terms:
-2x6 + 2x8 = 2x6 + -2x6

Combine like terms: 2x6 + -2x6 = 0
-2x6 + 2x8 = 0

Factor out the Greatest Common Factor (GCF), '2x6'.
2x6(-1 + x2) = 0

Factor a difference between two squares.
2x6((1 + x)(-1 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'x6' equal to zero and attempt to solve:

Simplifying
x6 = 0

Solving
x6 = 0

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

Simplifying
x6 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
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 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
Solution
x = {-1, 1}