18S^2+3S-9=12

Solution for 18S^2+3S-9=12 equation:

Simplifying
18S2 + 3S + -9 = 12

Reorder the terms:
-9 + 3S + 18S2 = 12

Solving
-9 + 3S + 18S2 = 12

Solving for variable 'S'.

Reorder the terms:
-9 + -12 + 3S + 18S2 = 12 + -12

Combine like terms: -9 + -12 = -21
-21 + 3S + 18S2 = 12 + -12

Combine like terms: 12 + -12 = 0
-21 + 3S + 18S2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + S + 6S2) = 0

Factor a trinomial.
3((-7 + -6S)(1 + -1S)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-7 + -6S)' equal to zero and attempt to solve:

Simplifying
-7 + -6S = 0

Solving
-7 + -6S = 0

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

Add '7' to each side of the equation.
-7 + 7 + -6S = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -6S = 0 + 7
-6S = 0 + 7

Combine like terms: 0 + 7 = 7
-6S = 7

Divide each side by '-6'.
S = -1.166666667

Simplifying
S = -1.166666667
Subproblem 2
Set the factor '(1 + -1S)' equal to zero and attempt to solve:

Simplifying
1 + -1S = 0

Solving
1 + -1S = 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 + -1S = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1S = 0 + -1
-1S = 0 + -1

Combine like terms: 0 + -1 = -1
-1S = -1

Divide each side by '-1'.
S = 1

Simplifying
S = 1
Solution
S = {-1.166666667, 1}