0=4h^2-8h-32-8h

Solution for 0=4h^2-8h-32-8h equation:

Simplifying
0 = 4h2 + -8h + -32 + -8h

Reorder the terms:
0 = -32 + -8h + -8h + 4h2

Combine like terms: -8h + -8h = -16h
0 = -32 + -16h + 4h2

Solving
0 = -32 + -16h + 4h2

Solving for variable 'h'.

Combine like terms: 0 + 32 = 32
32 + 16h + -4h2 = -32 + -16h + 4h2 + 32 + 16h + -4h2

Reorder the terms:
32 + 16h + -4h2 = -32 + 32 + -16h + 16h + 4h2 + -4h2

Combine like terms: -32 + 32 = 0
32 + 16h + -4h2 = 0 + -16h + 16h + 4h2 + -4h2
32 + 16h + -4h2 = -16h + 16h + 4h2 + -4h2

Combine like terms: -16h + 16h = 0
32 + 16h + -4h2 = 0 + 4h2 + -4h2
32 + 16h + -4h2 = 4h2 + -4h2

Combine like terms: 4h2 + -4h2 = 0
32 + 16h + -4h2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + 4h + -1h2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(8 + 4h + -1h2)' equal to zero and attempt to solve:

Simplifying
8 + 4h + -1h2 = 0

Solving
8 + 4h + -1h2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-8 + -4h + h2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -4h + 8 + h2 = 0 + 8

Reorder the terms:
-8 + 8 + -4h + h2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -4h + h2 = 0 + 8
-4h + h2 = 0 + 8

Combine like terms: 0 + 8 = 8
-4h + h2 = 8

The h term is -4h.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4h + 4 + h2 = 8 + 4

Reorder the terms:
4 + -4h + h2 = 8 + 4

Combine like terms: 8 + 4 = 12
4 + -4h + h2 = 12

Factor a perfect square on the left side:
(h + -2)(h + -2) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(h + -2) equal to 3.464101615 and -3.464101615.

Subproblem 1
h + -2 = 3.464101615

Simplifying
h + -2 = 3.464101615

Reorder the terms:
-2 + h = 3.464101615

Solving
-2 + h = 3.464101615

Solving for variable 'h'.

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

Add '2' to each side of the equation.
-2 + 2 + h = 3.464101615 + 2

Combine like terms: -2 + 2 = 0
0 + h = 3.464101615 + 2
h = 3.464101615 + 2

Combine like terms: 3.464101615 + 2 = 5.464101615
h = 5.464101615

Simplifying
h = 5.464101615

Subproblem 2
h + -2 = -3.464101615

Simplifying
h + -2 = -3.464101615

Reorder the terms:
-2 + h = -3.464101615

Solving
-2 + h = -3.464101615

Solving for variable 'h'.

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

Add '2' to each side of the equation.
-2 + 2 + h = -3.464101615 + 2

Combine like terms: -2 + 2 = 0
0 + h = -3.464101615 + 2
h = -3.464101615 + 2

Combine like terms: -3.464101615 + 2 = -1.464101615
h = -1.464101615

Simplifying
h = -1.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {5.464101615, -1.464101615}
Solution
h = {5.464101615, -1.464101615}