2h^2+12h-32=0

Solution for 2h^2+12h-32=0 equation:

Simplifying
2h2 + 12h + -32 = 0

Reorder the terms:
-32 + 12h + 2h2 = 0

Solving
-32 + 12h + 2h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + 6h + h2) = 0

Factor a trinomial.
2((-8 + -1h)(2 + -1h)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -1h)' equal to zero and attempt to solve:

Simplifying
-8 + -1h = 0

Solving
-8 + -1h = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1h = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1h = 0 + 8
-1h = 0 + 8

Combine like terms: 0 + 8 = 8
-1h = 8

Divide each side by '-1'.
h = -8

Simplifying
h = -8
Subproblem 2
Set the factor '(2 + -1h)' equal to zero and attempt to solve:

Simplifying
2 + -1h = 0

Solving
2 + -1h = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1h = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1h = 0 + -2
-1h = 0 + -2

Combine like terms: 0 + -2 = -2
-1h = -2

Divide each side by '-1'.
h = 2

Simplifying
h = 2
Solution
h = {-8, 2}