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

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

Simplifying
0 = x10 + -2x6 + x2

Reorder the terms:
0 = x2 + -2x6 + x10

Solving
0 = x2 + -2x6 + x10

Solving for variable 'x'.
Remove the zero:
-1x2 + 2x6 + -1x10 = x2 + -2x6 + x10 + -1x2 + 2x6 + -1x10

Reorder the terms:
-1x2 + 2x6 + -1x10 = x2 + -1x2 + -2x6 + 2x6 + x10 + -1x10

Combine like terms: x2 + -1x2 = 0
-1x2 + 2x6 + -1x10 = 0 + -2x6 + 2x6 + x10 + -1x10
-1x2 + 2x6 + -1x10 = -2x6 + 2x6 + x10 + -1x10

Combine like terms: -2x6 + 2x6 = 0
-1x2 + 2x6 + -1x10 = 0 + x10 + -1x10
-1x2 + 2x6 + -1x10 = x10 + -1x10

Combine like terms: x10 + -1x10 = 0
-1x2 + 2x6 + -1x10 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-1 + 2x4 + -1x8) = 0

Factor a trinomial.
x2((-1 + x4)(1 + -1x4)) = 0

Factor a difference between two squares.
x2(((1 + x2)(-1 + x2))(1 + -1x4)) = 0

Factor a difference between two squares.
x2(((1 + x2)((1 + x)(-1 + x)))(1 + -1x4)) = 0

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

Factor a difference between two squares.
x2(((1 + x2)((1 + x)(1 + -1x)))(1 + x2)(1 + x)(-1 + x)) = 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 + 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 5
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 6
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 7
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, -1, 1}