p^7-p=0

Solution for p^7-p=0 equation:

Simplifying
p7 + -1p = 0

Reorder the terms:
-1p + p7 = 0

Solving
-1p + p7 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'p'.
p(-1 + p6) = 0

Factor a difference between two squares.
p((1 + p3)(-1 + p3)) = 0

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

Simplifying
p = 0

Solving
p = 0

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

Simplifying
p = 0
Subproblem 2
Set the factor '(1 + p3)' equal to zero and attempt to solve:

Simplifying
1 + p3 = 0

Solving
1 + p3 = 0

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

Add '-1' to each side of the equation.
1 + -1 + p3 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + p3 = 0 + -1
p3 = 0 + -1

Combine like terms: 0 + -1 = -1
p3 = -1

Simplifying
p3 = -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 + p3)' equal to zero and attempt to solve:

Simplifying
-1 + p3 = 0

Solving
-1 + p3 = 0

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

Add '1' to each side of the equation.
-1 + 1 + p3 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + p3 = 0 + 1
p3 = 0 + 1

Combine like terms: 0 + 1 = 1
p3 = 1

Simplifying
p3 = 1

The solution to this equation could not be determined.

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