12s^2-27s-27=0

Solution for 12s^2-27s-27=0 equation:

Simplifying
12s2 + -27s + -27 = 0

Reorder the terms:
-27 + -27s + 12s2 = 0

Solving
-27 + -27s + 12s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + -9s + 4s2) = 0

Factor a trinomial.
3((-3 + -4s)(3 + -1s)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-3 + -4s)' equal to zero and attempt to solve:

Simplifying
-3 + -4s = 0

Solving
-3 + -4s = 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 + -4s = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4s = 0 + 3
-4s = 0 + 3

Combine like terms: 0 + 3 = 3
-4s = 3

Divide each side by '-4'.
s = -0.75

Simplifying
s = -0.75
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 = {-0.75, 3}