a^7-a=0

Solution for a^7-a=0 equation:

Simplifying
a7 + -1a = 0

Reorder the terms:
-1a + a7 = 0

Solving
-1a + a7 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(-1 + a6) = 0

Factor a difference between two squares.
a((1 + a3)(-1 + a3)) = 0

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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(1 + a3)' equal to zero and attempt to solve:

Simplifying
1 + a3 = 0

Solving
1 + a3 = 0

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

Add '-1' to each side of the equation.
1 + -1 + a3 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + a3 = 0 + -1
a3 = 0 + -1

Combine like terms: 0 + -1 = -1
a3 = -1

Simplifying
a3 = -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 + a3)' equal to zero and attempt to solve:

Simplifying
-1 + a3 = 0

Solving
-1 + a3 = 0

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

Add '1' to each side of the equation.
-1 + 1 + a3 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + a3 = 0 + 1
a3 = 0 + 1

Combine like terms: 0 + 1 = 1
a3 = 1

Simplifying
a3 = 1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}