900=5((35-6H)*(34+4H))

Solution for 900=5((35-6H)*(34+4H)) equation:

Simplifying
900 = 5((35 + -6H)(34 + 4H))

Multiply (35 + -6H) * (34 + 4H)
900 = 5((35(34 + 4H) + -6H * (34 + 4H)))
900 = 5(((34 * 35 + 4H * 35) + -6H * (34 + 4H)))
900 = 5(((1190 + 140H) + -6H * (34 + 4H)))
900 = 5((1190 + 140H + (34 * -6H + 4H * -6H)))
900 = 5((1190 + 140H + (-204H + -24H2)))

Combine like terms: 140H + -204H = -64H
900 = 5((1190 + -64H + -24H2))
900 = (1190 * 5 + -64H * 5 + -24H2 * 5)
900 = (5950 + -320H + -120H2)

Solving
900 = 5950 + -320H + -120H2

Solving for variable 'H'.

Combine like terms: 900 + -5950 = -5050
-5050 + 320H + 120H2 = 5950 + -320H + -120H2 + -5950 + 320H + 120H2

Reorder the terms:
-5050 + 320H + 120H2 = 5950 + -5950 + -320H + 320H + -120H2 + 120H2

Combine like terms: 5950 + -5950 = 0
-5050 + 320H + 120H2 = 0 + -320H + 320H + -120H2 + 120H2
-5050 + 320H + 120H2 = -320H + 320H + -120H2 + 120H2

Combine like terms: -320H + 320H = 0
-5050 + 320H + 120H2 = 0 + -120H2 + 120H2
-5050 + 320H + 120H2 = -120H2 + 120H2

Combine like terms: -120H2 + 120H2 = 0
-5050 + 320H + 120H2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-505 + 32H + 12H2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-505 + 32H + 12H2)' equal to zero and attempt to solve:

Simplifying
-505 + 32H + 12H2 = 0

Solving
-505 + 32H + 12H2 = 0

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

Divide each side by '12'.
-42.08333333 + 2.666666667H + H2 = 0

Move the constant term to the right:

Add '42.08333333' to each side of the equation.
-42.08333333 + 2.666666667H + 42.08333333 + H2 = 0 + 42.08333333

Reorder the terms:
-42.08333333 + 42.08333333 + 2.666666667H + H2 = 0 + 42.08333333

Combine like terms: -42.08333333 + 42.08333333 = 0.00000000
0.00000000 + 2.666666667H + H2 = 0 + 42.08333333
2.666666667H + H2 = 0 + 42.08333333

Combine like terms: 0 + 42.08333333 = 42.08333333
2.666666667H + H2 = 42.08333333

The H term is 2.666666667H.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667H + 1.777777780 + H2 = 42.08333333 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667H + H2 = 42.08333333 + 1.777777780

Combine like terms: 42.08333333 + 1.777777780 = 43.86111111
1.777777780 + 2.666666667H + H2 = 43.86111111

Factor a perfect square on the left side:
(H + 1.333333334)(H + 1.333333334) = 43.86111111

Calculate the square root of the right side: 6.622772162

Break this problem into two subproblems by setting 
(H + 1.333333334) equal to 6.622772162 and -6.622772162.

Subproblem 1
H + 1.333333334 = 6.622772162

Simplifying
H + 1.333333334 = 6.622772162

Reorder the terms:
1.333333334 + H = 6.622772162

Solving
1.333333334 + H = 6.622772162

Solving for variable 'H'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + H = 6.622772162 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + H = 6.622772162 + -1.333333334
H = 6.622772162 + -1.333333334

Combine like terms: 6.622772162 + -1.333333334 = 5.289438828
H = 5.289438828

Simplifying
H = 5.289438828

Subproblem 2
H + 1.333333334 = -6.622772162

Simplifying
H + 1.333333334 = -6.622772162

Reorder the terms:
1.333333334 + H = -6.622772162

Solving
1.333333334 + H = -6.622772162

Solving for variable 'H'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + H = -6.622772162 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + H = -6.622772162 + -1.333333334
H = -6.622772162 + -1.333333334

Combine like terms: -6.622772162 + -1.333333334 = -7.956105496
H = -7.956105496

Simplifying
H = -7.956105496

Solution
The solution to the problem is based on the solutions
from the subproblems.
H = {5.289438828, -7.956105496}
Solution
H = {5.289438828, -7.956105496}