a^4+a+a^4+a=

Solution for a^4+a+a^4+a= equation:

Simplifying
a4 + a + a4 + a = 0

Reorder the terms:
a + a + a4 + a4 = 0

Combine like terms: a + a = 2a
2a + a4 + a4 = 0

Combine like terms: a4 + a4 = 2a4
2a + 2a4 = 0

Solving
2a + 2a4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a'.
2a(1 + a3) = 0

Ignore the factor 2.
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.
Solution
a = {0}