0=x^6-x^2

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Solution for 0=x^6-x^2 equation: 


Simplifying
0 = x6 + -1x2

Reorder the terms:
0 = -1x2 + x6

Solving
0 = -1x2 + x6

Solving for variable 'x'.
Remove the zero:
x2 + -1x6 = -1x2 + x6 + x2 + -1x6

Reorder the terms:
x2 + -1x6 = -1x2 + x2 + x6 + -1x6

Combine like terms: -1x2 + x2 = 0
x2 + -1x6 = 0 + x6 + -1x6
x2 + -1x6 = x6 + -1x6

Combine like terms: x6 + -1x6 = 0
x2 + -1x6 = 0

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

Factor a difference between two squares.
x2((1 + x2)(1 + -1x2)) = 0

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

Simplifying
1 + x2 = 0

Solving
1 + x2 = 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 + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x2 = 0 + -1
x2 = 0 + -1

Combine like terms: 0 + -1 = -1
x2 = -1

Simplifying
x2 = -1

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}

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