(c^2)=c^10

Solution for (c^2)=c^10 equation:

Simplifying
(c2) = c10
c2 = c10

Solving
c2 = c10

Solving for variable 'c'.

Combine like terms: c10 + -1c10 = 0
c2 + -1c10 = 0

Factor out the Greatest Common Factor (GCF), 'c2'.
c2(1 + -1c8) = 0

Factor a difference between two squares.
c2((1 + c4)(1 + -1c4)) = 0

Factor a difference between two squares.
c2((1 + c4)((1 + c2)(1 + -1c2))) = 0

Factor a difference between two squares.
c2((1 + c4)((1 + c2)((1 + c)(1 + -1c)))) = 0

Subproblem 1
Set the factor 'c2' equal to zero and attempt to solve:

Simplifying
c2 = 0

Solving
c2 = 0

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

Simplifying
c2 = 0

Take the square root of each side:
c = {0}
Subproblem 2
Set the factor '(1 + c4)' equal to zero and attempt to solve:

Simplifying
1 + c4 = 0

Solving
1 + c4 = 0

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

Add '-1' to each side of the equation.
1 + -1 + c4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + c4 = 0 + -1
c4 = 0 + -1

Combine like terms: 0 + -1 = -1
c4 = -1

Simplifying
c4 = -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 + c2)' equal to zero and attempt to solve:

Simplifying
1 + c2 = 0

Solving
1 + c2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + c2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + c2 = 0 + -1
c2 = 0 + -1

Combine like terms: 0 + -1 = -1
c2 = -1

Simplifying
c2 = -1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 4
Set the factor '(1 + c)' equal to zero and attempt to solve:

Simplifying
1 + c = 0

Solving
1 + c = 0

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

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

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

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

Simplifying
c = -1
Subproblem 5
Set the factor '(1 + -1c)' equal to zero and attempt to solve:

Simplifying
1 + -1c = 0

Solving
1 + -1c = 0

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

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

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

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

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

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