4u^5+22u^4+10u^3=0

Solution for 4u^5+22u^4+10u^3=0 equation:

Simplifying
4u5 + 22u4 + 10u3 = 0

Reorder the terms:
10u3 + 22u4 + 4u5 = 0

Solving
10u3 + 22u4 + 4u5 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2u3'.
2u3(5 + 11u + 2u2) = 0

Factor a trinomial.
2u3((5 + u)(1 + 2u)) = 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 '(5 + u)' equal to zero and attempt to solve:

Simplifying
5 + u = 0

Solving
5 + u = 0

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

Add '-5' to each side of the equation.
5 + -5 + u = 0 + -5

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

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

Simplifying
u = -5
Subproblem 3
Set the factor '(1 + 2u)' equal to zero and attempt to solve:

Simplifying
1 + 2u = 0

Solving
1 + 2u = 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 + 2u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2u = 0 + -1
2u = 0 + -1

Combine like terms: 0 + -1 = -1
2u = -1

Divide each side by '2'.
u = -0.5

Simplifying
u = -0.5
Solution
u = {-5, -0.5}