16h-4h(5h-7)=4

Solution for 16h-4h(5h-7)=4 equation:

Simplifying
16h + -4h(5h + -7) = 4

Reorder the terms:
16h + -4h(-7 + 5h) = 4
16h + (-7 * -4h + 5h * -4h) = 4
16h + (28h + -20h2) = 4

Combine like terms: 16h + 28h = 44h
44h + -20h2 = 4

Solving
44h + -20h2 = 4

Solving for variable 'h'.

Reorder the terms:
-4 + 44h + -20h2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 44h + -20h2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 11h + -5h2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + 11h + -5h2)' equal to zero and attempt to solve:

Simplifying
-1 + 11h + -5h2 = 0

Solving
-1 + 11h + -5h2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
0.2 + -2.2h + h2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + -2.2h + -0.2 + h2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + -2.2h + h2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + -2.2h + h2 = 0 + -0.2
-2.2h + h2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
-2.2h + h2 = -0.2

The h term is -2.2h.  Take half its coefficient (-1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
-2.2h + 1.21 + h2 = -0.2 + 1.21

Reorder the terms:
1.21 + -2.2h + h2 = -0.2 + 1.21

Combine like terms: -0.2 + 1.21 = 1.01
1.21 + -2.2h + h2 = 1.01

Factor a perfect square on the left side:
(h + -1.1)(h + -1.1) = 1.01

Calculate the square root of the right side: 1.004987562

Break this problem into two subproblems by setting 
(h + -1.1) equal to 1.004987562 and -1.004987562.

Subproblem 1
h + -1.1 = 1.004987562

Simplifying
h + -1.1 = 1.004987562

Reorder the terms:
-1.1 + h = 1.004987562

Solving
-1.1 + h = 1.004987562

Solving for variable 'h'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + h = 1.004987562 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + h = 1.004987562 + 1.1
h = 1.004987562 + 1.1

Combine like terms: 1.004987562 + 1.1 = 2.104987562
h = 2.104987562

Simplifying
h = 2.104987562

Subproblem 2
h + -1.1 = -1.004987562

Simplifying
h + -1.1 = -1.004987562

Reorder the terms:
-1.1 + h = -1.004987562

Solving
-1.1 + h = -1.004987562

Solving for variable 'h'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + h = -1.004987562 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + h = -1.004987562 + 1.1
h = -1.004987562 + 1.1

Combine like terms: -1.004987562 + 1.1 = 0.095012438
h = 0.095012438

Simplifying
h = 0.095012438

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {2.104987562, 0.095012438}
Solution
h = {2.104987562, 0.095012438}