6s^2+59s+75=0

Solution for 6s^2+59s+75=0 equation:

Simplifying
6s2 + 59s + 75 = 0

Reorder the terms:
75 + 59s + 6s2 = 0

Solving
75 + 59s + 6s2 = 0

Solving for variable 's'.

Factor a trinomial.
(25 + 3s)(3 + 2s) = 0

Subproblem 1
Set the factor '(25 + 3s)' equal to zero and attempt to solve:

Simplifying
25 + 3s = 0

Solving
25 + 3s = 0

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

Add '-25' to each side of the equation.
25 + -25 + 3s = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 3s = 0 + -25
3s = 0 + -25

Combine like terms: 0 + -25 = -25
3s = -25

Divide each side by '3'.
s = -8.333333333

Simplifying
s = -8.333333333
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 = {-8.333333333, -1.5}