5s^2+13s+6=0

Solution for 5s^2+13s+6=0 equation:

Simplifying
5s2 + 13s + 6 = 0

Reorder the terms:
6 + 13s + 5s2 = 0

Solving
6 + 13s + 5s2 = 0

Solving for variable 's'.

Factor a trinomial.
(2 + s)(3 + 5s) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + 5s)' equal to zero and attempt to solve:

Simplifying
3 + 5s = 0

Solving
3 + 5s = 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 + 5s = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5s = 0 + -3
5s = 0 + -3

Combine like terms: 0 + -3 = -3
5s = -3

Divide each side by '5'.
s = -0.6

Simplifying
s = -0.6
Solution
s = {-2, -0.6}