6u^6+24u^5+24u^4=0

Solution for 6u^6+24u^5+24u^4=0 equation:

Simplifying
6u6 + 24u5 + 24u4 = 0

Reorder the terms:
24u4 + 24u5 + 6u6 = 0

Solving
24u4 + 24u5 + 6u6 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '6u4'.
6u4(4 + 4u + u2) = 0

Factor a trinomial.
6u4((2 + u)(2 + u)) = 0

Ignore the factor 6.
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}