5s^2+33s+40=0

Solution for 5s^2+33s+40=0 equation:

Simplifying
5s2 + 33s + 40 = 0

Reorder the terms:
40 + 33s + 5s2 = 0

Solving
40 + 33s + 5s2 = 0

Solving for variable 's'.

Factor a trinomial.
(5 + s)(8 + 5s) = 0

Subproblem 1
Set the factor '(5 + s)' equal to zero and attempt to solve:

Simplifying
5 + s = 0

Solving
5 + s = 0

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

Add '-5' to each side of the equation.
5 + -5 + s = 0 + -5

Combine like terms: 5 + -5 = 0
0 + s = 0 + -5
s = 0 + -5

Combine like terms: 0 + -5 = -5
s = -5

Simplifying
s = -5
Subproblem 2
Set the factor '(8 + 5s)' equal to zero and attempt to solve:

Simplifying
8 + 5s = 0

Solving
8 + 5s = 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 + 5s = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5s = 0 + -8
5s = 0 + -8

Combine like terms: 0 + -8 = -8
5s = -8

Divide each side by '5'.
s = -1.6

Simplifying
s = -1.6
Solution
s = {-5, -1.6}