3h^2-39h=-126

Solution for 3h^2-39h=-126 equation:

Simplifying
3h2 + -39h = -126

Reorder the terms:
-39h + 3h2 = -126

Solving
-39h + 3h2 = -126

Solving for variable 'h'.

Reorder the terms:
126 + -39h + 3h2 = -126 + 126

Combine like terms: -126 + 126 = 0
126 + -39h + 3h2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(42 + -13h + h2) = 0

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

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

Simplifying
6 + -1h = 0

Solving
6 + -1h = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1h = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1h = 0 + -6
-1h = 0 + -6

Combine like terms: 0 + -6 = -6
-1h = -6

Divide each side by '-1'.
h = 6

Simplifying
h = 6
Subproblem 2
Set the factor '(7 + -1h)' equal to zero and attempt to solve:

Simplifying
7 + -1h = 0

Solving
7 + -1h = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1h = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1h = 0 + -7
-1h = 0 + -7

Combine like terms: 0 + -7 = -7
-1h = -7

Divide each side by '-1'.
h = 7

Simplifying
h = 7
Solution
h = {6, 7}