s^5+4s^4+4s^3=0

Solution for s^5+4s^4+4s^3=0 equation:

Simplifying
s5 + 4s4 + 4s3 = 0

Reorder the terms:
4s3 + 4s4 + s5 = 0

Solving
4s3 + 4s4 + s5 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), 's3'.
s3(4 + 4s + s2) = 0

Factor a trinomial.
s3((2 + s)(2 + s)) = 0

Subproblem 1
Set the factor 's3' equal to zero and attempt to solve:

Simplifying
s3 = 0

Solving
s3 = 0

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

Simplifying
s3 = 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 + s)' equal to zero and attempt to solve:

Simplifying
2 + s = 0

Solving
2 + s = 0

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

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

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

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

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

Simplifying
2 + s = 0

Solving
2 + s = 0

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

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

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

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

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