3(2h-5)4(3h+2)=11

Solution for 3(2h-5)4(3h+2)=11 equation:

Simplifying
3(2h + -5) * 4(3h + 2) = 11

Reorder the terms:
3(-5 + 2h) * 4(3h + 2) = 11

Reorder the terms:
3(-5 + 2h) * 4(2 + 3h) = 11

Reorder the terms for easier multiplication:
3 * 4(-5 + 2h)(2 + 3h) = 11

Multiply 3 * 4
12(-5 + 2h)(2 + 3h) = 11

Multiply (-5 + 2h) * (2 + 3h)
12(-5(2 + 3h) + 2h * (2 + 3h)) = 11
12((2 * -5 + 3h * -5) + 2h * (2 + 3h)) = 11
12((-10 + -15h) + 2h * (2 + 3h)) = 11
12(-10 + -15h + (2 * 2h + 3h * 2h)) = 11
12(-10 + -15h + (4h + 6h2)) = 11

Combine like terms: -15h + 4h = -11h
12(-10 + -11h + 6h2) = 11
(-10 * 12 + -11h * 12 + 6h2 * 12) = 11
(-120 + -132h + 72h2) = 11

Solving
-120 + -132h + 72h2 = 11

Solving for variable 'h'.

Reorder the terms:
-120 + -11 + -132h + 72h2 = 11 + -11

Combine like terms: -120 + -11 = -131
-131 + -132h + 72h2 = 11 + -11

Combine like terms: 11 + -11 = 0
-131 + -132h + 72h2 = 0

Begin completing the square.  Divide all terms by
72 the coefficient of the squared term: 

Divide each side by '72'.
-1.819444444 + -1.833333333h + h2 = 0

Move the constant term to the right:

Add '1.819444444' to each side of the equation.
-1.819444444 + -1.833333333h + 1.819444444 + h2 = 0 + 1.819444444

Reorder the terms:
-1.819444444 + 1.819444444 + -1.833333333h + h2 = 0 + 1.819444444

Combine like terms: -1.819444444 + 1.819444444 = 0.000000000
0.000000000 + -1.833333333h + h2 = 0 + 1.819444444
-1.833333333h + h2 = 0 + 1.819444444

Combine like terms: 0 + 1.819444444 = 1.819444444
-1.833333333h + h2 = 1.819444444

The h term is -1.833333333h.  Take half its coefficient (-0.9166666665).
Square it (0.8402777775) and add it to both sides.

Add '0.8402777775' to each side of the equation.
-1.833333333h + 0.8402777775 + h2 = 1.819444444 + 0.8402777775

Reorder the terms:
0.8402777775 + -1.833333333h + h2 = 1.819444444 + 0.8402777775

Combine like terms: 1.819444444 + 0.8402777775 = 2.6597222215
0.8402777775 + -1.833333333h + h2 = 2.6597222215

Factor a perfect square on the left side:
(h + -0.9166666665)(h + -0.9166666665) = 2.6597222215

Calculate the square root of the right side: 1.630865482

Break this problem into two subproblems by setting 
(h + -0.9166666665) equal to 1.630865482 and -1.630865482.

Subproblem 1
h + -0.9166666665 = 1.630865482

Simplifying
h + -0.9166666665 = 1.630865482

Reorder the terms:
-0.9166666665 + h = 1.630865482

Solving
-0.9166666665 + h = 1.630865482

Solving for variable 'h'.

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

Add '0.9166666665' to each side of the equation.
-0.9166666665 + 0.9166666665 + h = 1.630865482 + 0.9166666665

Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000
0.0000000000 + h = 1.630865482 + 0.9166666665
h = 1.630865482 + 0.9166666665

Combine like terms: 1.630865482 + 0.9166666665 = 2.5475321485
h = 2.5475321485

Simplifying
h = 2.5475321485

Subproblem 2
h + -0.9166666665 = -1.630865482

Simplifying
h + -0.9166666665 = -1.630865482

Reorder the terms:
-0.9166666665 + h = -1.630865482

Solving
-0.9166666665 + h = -1.630865482

Solving for variable 'h'.

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

Add '0.9166666665' to each side of the equation.
-0.9166666665 + 0.9166666665 + h = -1.630865482 + 0.9166666665

Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000
0.0000000000 + h = -1.630865482 + 0.9166666665
h = -1.630865482 + 0.9166666665

Combine like terms: -1.630865482 + 0.9166666665 = -0.7141988155
h = -0.7141988155

Simplifying
h = -0.7141988155

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {2.5475321485, -0.7141988155}