6s^2-9s-6=0

Solution for 6s^2-9s-6=0 equation:

Simplifying
6s2 + -9s + -6 = 0

Reorder the terms:
-6 + -9s + 6s2 = 0

Solving
-6 + -9s + 6s2 = 0

Solving for variable 's'.

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

Factor a trinomial.
3((-1 + -2s)(2 + -1s)) = 0

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

Simplifying
-1 + -2s = 0

Solving
-1 + -2s = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2s = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2s = 0 + 1
-2s = 0 + 1

Combine like terms: 0 + 1 = 1
-2s = 1

Divide each side by '-2'.
s = -0.5

Simplifying
s = -0.5
Subproblem 2
Set the factor '(2 + -1s)' equal to zero and attempt to solve:

Simplifying
2 + -1s = 0

Solving
2 + -1s = 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 + -1s = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1s = 0 + -2
-1s = 0 + -2

Combine like terms: 0 + -2 = -2
-1s = -2

Divide each side by '-1'.
s = 2

Simplifying
s = 2
Solution
s = {-0.5, 2}