8u^6+32u^5+32u^4=0

Solution for 8u^6+32u^5+32u^4=0 equation:

Simplifying
8u6 + 32u5 + 32u4 = 0

Reorder the terms:
32u4 + 32u5 + 8u6 = 0

Solving
32u4 + 32u5 + 8u6 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '8u4'.
8u4(4 + 4u + u2) = 0

Factor a trinomial.
8u4((2 + u)(2 + u)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor 'u4' equal to zero and attempt to solve:

Simplifying
u4 = 0

Solving
u4 = 0

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

Simplifying
u4 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(2 + u)' equal to zero and attempt to solve:

Simplifying
2 + u = 0

Solving
2 + u = 0

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

Add '-2' to each side of the equation.
2 + -2 + u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + u = 0 + -2
u = 0 + -2

Combine like terms: 0 + -2 = -2
u = -2

Simplifying
u = -2
Subproblem 3
Set the factor '(2 + u)' equal to zero and attempt to solve:

Simplifying
2 + u = 0

Solving
2 + u = 0

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

Add '-2' to each side of the equation.
2 + -2 + u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + u = 0 + -2
u = 0 + -2

Combine like terms: 0 + -2 = -2
u = -2

Simplifying
u = -2
Solution
u = {-2, -2}