9h^2-108h-117=0

Solution for 9h^2-108h-117=0 equation:

Simplifying
9h2 + -108h + -117 = 0

Reorder the terms:
-117 + -108h + 9h2 = 0

Solving
-117 + -108h + 9h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-13 + -12h + h2) = 0

Factor a trinomial.
9((-1 + -1h)(13 + -1h)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(-1 + -1h)' equal to zero and attempt to solve:

Simplifying
-1 + -1h = 0

Solving
-1 + -1h = 0

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

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

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

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

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

Simplifying
h = -1
Subproblem 2
Set the factor '(13 + -1h)' equal to zero and attempt to solve:

Simplifying
13 + -1h = 0

Solving
13 + -1h = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1h = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1h = 0 + -13
-1h = 0 + -13

Combine like terms: 0 + -13 = -13
-1h = -13

Divide each side by '-1'.
h = 13

Simplifying
h = 13
Solution
h = {-1, 13}