u^4+u^2=0

Solution for u^4+u^2=0 equation:

Simplifying
u4 + u2 = 0

Reorder the terms:
u2 + u4 = 0

Solving
u2 + u4 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), 'u2'.
u2(1 + u2) = 0

Subproblem 1
Set the factor 'u2' equal to zero and attempt to solve:

Simplifying
u2 = 0

Solving
u2 = 0

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

Simplifying
u2 = 0

Take the square root of each side:
u = {0}
Subproblem 2
Set the factor '(1 + u2)' equal to zero and attempt to solve:

Simplifying
1 + u2 = 0

Solving
1 + u2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + u2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + u2 = 0 + -1
u2 = 0 + -1

Combine like terms: 0 + -1 = -1
u2 = -1

Simplifying
u2 = -1

The solution to this equation could not be determined.

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