3h^2+6h-135=0

Solution for 3h^2+6h-135=0 equation:

Simplifying
3h2 + 6h + -135 = 0

Reorder the terms:
-135 + 6h + 3h2 = 0

Solving
-135 + 6h + 3h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-45 + 2h + h2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-45 + 2h + h2)' equal to zero and attempt to solve:

Simplifying
-45 + 2h + h2 = 0

Solving
-45 + 2h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 2h + 45 + h2 = 0 + 45

Reorder the terms:
-45 + 45 + 2h + h2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 2h + h2 = 0 + 45
2h + h2 = 0 + 45

Combine like terms: 0 + 45 = 45
2h + h2 = 45

The h term is 2h.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2h + 1 + h2 = 45 + 1

Reorder the terms:
1 + 2h + h2 = 45 + 1

Combine like terms: 45 + 1 = 46
1 + 2h + h2 = 46

Factor a perfect square on the left side:
(h + 1)(h + 1) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(h + 1) equal to 6.782329983 and -6.782329983.

Subproblem 1
h + 1 = 6.782329983

Simplifying
h + 1 = 6.782329983

Reorder the terms:
1 + h = 6.782329983

Solving
1 + h = 6.782329983

Solving for variable 'h'.

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

Add '-1' to each side of the equation.
1 + -1 + h = 6.782329983 + -1

Combine like terms: 1 + -1 = 0
0 + h = 6.782329983 + -1
h = 6.782329983 + -1

Combine like terms: 6.782329983 + -1 = 5.782329983
h = 5.782329983

Simplifying
h = 5.782329983

Subproblem 2
h + 1 = -6.782329983

Simplifying
h + 1 = -6.782329983

Reorder the terms:
1 + h = -6.782329983

Solving
1 + h = -6.782329983

Solving for variable 'h'.

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

Add '-1' to each side of the equation.
1 + -1 + h = -6.782329983 + -1

Combine like terms: 1 + -1 = 0
0 + h = -6.782329983 + -1
h = -6.782329983 + -1

Combine like terms: -6.782329983 + -1 = -7.782329983
h = -7.782329983

Simplifying
h = -7.782329983

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {5.782329983, -7.782329983}
Solution
h = {5.782329983, -7.782329983}