y^6+y=0

Solution for y^6+y=0 equation:

Simplifying
y6 + y = 0

Reorder the terms:
y + y6 = 0

Solving
y + y6 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(1 + y5) = 0

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

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(1 + y5)' equal to zero and attempt to solve:

Simplifying
1 + y5 = 0

Solving
1 + y5 = 0

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

Add '-1' to each side of the equation.
1 + -1 + y5 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + y5 = 0 + -1
y5 = 0 + -1

Combine like terms: 0 + -1 = -1
y5 = -1

Simplifying
y5 = -1

The solution to this equation could not be determined.

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