(s+2)(s+4)(s)=0

Solution for (s+2)(s+4)(s)=0 equation:

Simplifying
(s + 2)(s + 4)(s) = 0

Reorder the terms:
(2 + s)(s + 4)(s) = 0

Reorder the terms:
(2 + s)(4 + s)(s) = 0

Reorder the terms for easier multiplication:
s(2 + s)(4 + s) = 0

Multiply (2 + s) * (4 + s)
s(2(4 + s) + s(4 + s)) = 0
s((4 * 2 + s * 2) + s(4 + s)) = 0
s((8 + 2s) + s(4 + s)) = 0
s(8 + 2s + (4 * s + s * s)) = 0
s(8 + 2s + (4s + s2)) = 0

Combine like terms: 2s + 4s = 6s
s(8 + 6s + s2) = 0
(8 * s + 6s * s + s2 * s) = 0
(8s + 6s2 + s3) = 0

Solving
8s + 6s2 + s3 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), 's'.
s(8 + 6s + s2) = 0

Factor a trinomial.
s((4 + s)(2 + 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 '(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
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 = {0, -4, -2}