s^3+10s^2+24s=0

Solution for s^3+10s^2+24s=0 equation:

Simplifying
s3 + 10s2 + 24s = 0

Reorder the terms:
24s + 10s2 + s3 = 0

Solving
24s + 10s2 + s3 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), 's'.
s(24 + 10s + s2) = 0

Factor a trinomial.
s((6 + s)(4 + s)) = 0

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

Simplifying
s = 0

Solving
s = 0

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

Simplifying
s = 0
Subproblem 2
Set the factor '(6 + s)' equal to zero and attempt to solve:

Simplifying
6 + s = 0

Solving
6 + s = 0

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

Add '-6' to each side of the equation.
6 + -6 + s = 0 + -6

Combine like terms: 6 + -6 = 0
0 + s = 0 + -6
s = 0 + -6

Combine like terms: 0 + -6 = -6
s = -6

Simplifying
s = -6
Subproblem 3
Set the factor '(4 + s)' equal to zero and attempt to solve:

Simplifying
4 + s = 0

Solving
4 + s = 0

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

Add '-4' to each side of the equation.
4 + -4 + s = 0 + -4

Combine like terms: 4 + -4 = 0
0 + s = 0 + -4
s = 0 + -4

Combine like terms: 0 + -4 = -4
s = -4

Simplifying
s = -4
Solution
s = {0, -6, -4}