2(h-8)h=h-16

Solution for 2(h-8)h=h-16 equation:

Simplifying
2(h + -8) * h = h + -16

Reorder the terms:
2(-8 + h) * h = h + -16

Reorder the terms for easier multiplication:
2h(-8 + h) = h + -16
(-8 * 2h + h * 2h) = h + -16
(-16h + 2h2) = h + -16

Reorder the terms:
-16h + 2h2 = -16 + h

Solving
-16h + 2h2 = -16 + h

Solving for variable 'h'.

Reorder the terms:
16 + -16h + -1h + 2h2 = -16 + h + 16 + -1h

Combine like terms: -16h + -1h = -17h
16 + -17h + 2h2 = -16 + h + 16 + -1h

Reorder the terms:
16 + -17h + 2h2 = -16 + 16 + h + -1h

Combine like terms: -16 + 16 = 0
16 + -17h + 2h2 = 0 + h + -1h
16 + -17h + 2h2 = h + -1h

Combine like terms: h + -1h = 0
16 + -17h + 2h2 = 0

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

Divide each side by '2'.
8 + -8.5h + h2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -8.5h + -8 + h2 = 0 + -8

Reorder the terms:
8 + -8 + -8.5h + h2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -8.5h + h2 = 0 + -8
-8.5h + h2 = 0 + -8

Combine like terms: 0 + -8 = -8
-8.5h + h2 = -8

The h term is -8.5h.  Take half its coefficient (-4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
-8.5h + 18.0625 + h2 = -8 + 18.0625

Reorder the terms:
18.0625 + -8.5h + h2 = -8 + 18.0625

Combine like terms: -8 + 18.0625 = 10.0625
18.0625 + -8.5h + h2 = 10.0625

Factor a perfect square on the left side:
(h + -4.25)(h + -4.25) = 10.0625

Calculate the square root of the right side: 3.172144385

Break this problem into two subproblems by setting 
(h + -4.25) equal to 3.172144385 and -3.172144385.

Subproblem 1
h + -4.25 = 3.172144385

Simplifying
h + -4.25 = 3.172144385

Reorder the terms:
-4.25 + h = 3.172144385

Solving
-4.25 + h = 3.172144385

Solving for variable 'h'.

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

Add '4.25' to each side of the equation.
-4.25 + 4.25 + h = 3.172144385 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + h = 3.172144385 + 4.25
h = 3.172144385 + 4.25

Combine like terms: 3.172144385 + 4.25 = 7.422144385
h = 7.422144385

Simplifying
h = 7.422144385

Subproblem 2
h + -4.25 = -3.172144385

Simplifying
h + -4.25 = -3.172144385

Reorder the terms:
-4.25 + h = -3.172144385

Solving
-4.25 + h = -3.172144385

Solving for variable 'h'.

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

Add '4.25' to each side of the equation.
-4.25 + 4.25 + h = -3.172144385 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + h = -3.172144385 + 4.25
h = -3.172144385 + 4.25

Combine like terms: -3.172144385 + 4.25 = 1.077855615
h = 1.077855615

Simplifying
h = 1.077855615

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {7.422144385, 1.077855615}