6s^2+57s+72=0

Solution for 6s^2+57s+72=0 equation:

Simplifying
6s2 + 57s + 72 = 0

Reorder the terms:
72 + 57s + 6s2 = 0

Solving
72 + 57s + 6s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '3'.
3(24 + 19s + 2s2) = 0

Factor a trinomial.
3((8 + s)(3 + 2s)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(8 + s)' equal to zero and attempt to solve:

Simplifying
8 + s = 0

Solving
8 + s = 0

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

Add '-8' to each side of the equation.
8 + -8 + s = 0 + -8

Combine like terms: 8 + -8 = 0
0 + s = 0 + -8
s = 0 + -8

Combine like terms: 0 + -8 = -8
s = -8

Simplifying
s = -8
Subproblem 2
Set the factor '(3 + 2s)' equal to zero and attempt to solve:

Simplifying
3 + 2s = 0

Solving
3 + 2s = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2s = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2s = 0 + -3
2s = 0 + -3

Combine like terms: 0 + -3 = -3
2s = -3

Divide each side by '2'.
s = -1.5

Simplifying
s = -1.5
Solution
s = {-8, -1.5}