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 + -5s)(3 + -1s) = 0

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

Simplifying
-2 + -5s = 0

Solving
-2 + -5s = 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 + -5s = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5s = 0 + 2
-5s = 0 + 2

Combine like terms: 0 + 2 = 2
-5s = 2

Divide each side by '-5'.
s = -0.4

Simplifying
s = -0.4
Subproblem 2
Set the factor '(3 + -1s)' equal to zero and attempt to solve:

Simplifying
3 + -1s = 0

Solving
3 + -1s = 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 + -1s = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1s = 0 + -3
-1s = 0 + -3

Combine like terms: 0 + -3 = -3
-1s = -3

Divide each side by '-1'.
s = 3

Simplifying
s = 3
Solution
s = {-0.4, 3}