s^2+4s+6s+24=0

Solution for s^2+4s+6s+24=0 equation:

Simplifying
s2 + 4s + 6s + 24 = 0

Reorder the terms:
24 + 4s + 6s + s2 = 0

Combine like terms: 4s + 6s = 10s
24 + 10s + s2 = 0

Solving
24 + 10s + s2 = 0

Solving for variable 's'.

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

Subproblem 1
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 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
Solution
s = {-6, -4}