4u^4+22u^3+10u^2=0

Solution for 4u^4+22u^3+10u^2=0 equation:

Simplifying
4u4 + 22u3 + 10u2 = 0

Reorder the terms:
10u2 + 22u3 + 4u4 = 0

Solving
10u2 + 22u3 + 4u4 = 0

Solving for variable 'u'.

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

Factor a trinomial.
2u2((5 + u)(1 + 2u)) = 0

Ignore the factor 2.
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 '(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 = {0, -5, -0.5}