(12h^2-3h-15)=0

Solution for (12h^2-3h-15)=0 equation:

Simplifying
(12h2 + -3h + -15) = 0

Reorder the terms:
(-15 + -3h + 12h2) = 0

Remove parenthesis around (-15 + -3h + 12h2)
-15 + -3h + 12h2 = 0

Solving
-15 + -3h + 12h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -1h + 4h2) = 0

Factor a trinomial.
3((-1 + -1h)(5 + -4h)) = 0

Ignore the factor 3.
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 '(5 + -4h)' equal to zero and attempt to solve:

Simplifying
5 + -4h = 0

Solving
5 + -4h = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4h = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4h = 0 + -5
-4h = 0 + -5

Combine like terms: 0 + -5 = -5
-4h = -5

Divide each side by '-4'.
h = 1.25

Simplifying
h = 1.25
Solution
h = {-1, 1.25}