10u^5+32u^4+6u^3=0

Solution for 10u^5+32u^4+6u^3=0 equation:

Simplifying
10u5 + 32u4 + 6u3 = 0

Reorder the terms:
6u3 + 32u4 + 10u5 = 0

Solving
6u3 + 32u4 + 10u5 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2u3'.
2u3(3 + 16u + 5u2) = 0

Factor a trinomial.
2u3((3 + u)(1 + 5u)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'u3' equal to zero and attempt to solve:

Simplifying
u3 = 0

Solving
u3 = 0

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

Simplifying
u3 = 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 '(3 + u)' equal to zero and attempt to solve:

Simplifying
3 + u = 0

Solving
3 + u = 0

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

Add '-3' to each side of the equation.
3 + -3 + u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + u = 0 + -3
u = 0 + -3

Combine like terms: 0 + -3 = -3
u = -3

Simplifying
u = -3
Subproblem 3
Set the factor '(1 + 5u)' equal to zero and attempt to solve:

Simplifying
1 + 5u = 0

Solving
1 + 5u = 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 + 5u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5u = 0 + -1
5u = 0 + -1

Combine like terms: 0 + -1 = -1
5u = -1

Divide each side by '5'.
u = -0.2

Simplifying
u = -0.2
Solution
u = {-3, -0.2}