a^6+32a=0

Solution for a^6+32a=0 equation:

Simplifying
a6 + 32a = 0

Reorder the terms:
32a + a6 = 0

Solving
32a + a6 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(32 + a5) = 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 '(32 + a5)' equal to zero and attempt to solve:

Simplifying
32 + a5 = 0

Solving
32 + a5 = 0

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

Add '-32' to each side of the equation.
32 + -32 + a5 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + a5 = 0 + -32
a5 = 0 + -32

Combine like terms: 0 + -32 = -32
a5 = -32

Simplifying
a5 = -32

The solution to this equation could not be determined.

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