5h*2(11-h)=-5

Solution for 5h*2(11-h)=-5 equation:

Simplifying
5h * 2(11 + -1h) = -5

Reorder the terms for easier multiplication:
5 * 2h(11 + -1h) = -5

Multiply 5 * 2
10h(11 + -1h) = -5
(11 * 10h + -1h * 10h) = -5
(110h + -10h2) = -5

Solving
110h + -10h2 = -5

Solving for variable 'h'.

Reorder the terms:
5 + 110h + -10h2 = -5 + 5

Combine like terms: -5 + 5 = 0
5 + 110h + -10h2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(1 + 22h + -2h2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(1 + 22h + -2h2)' equal to zero and attempt to solve:

Simplifying
1 + 22h + -2h2 = 0

Solving
1 + 22h + -2h2 = 0

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

Divide each side by '-2'.
-0.5 + -11h + h2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -11h + 0.5 + h2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -11h + h2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -11h + h2 = 0 + 0.5
-11h + h2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-11h + h2 = 0.5

The h term is -11h.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11h + 30.25 + h2 = 0.5 + 30.25

Reorder the terms:
30.25 + -11h + h2 = 0.5 + 30.25

Combine like terms: 0.5 + 30.25 = 30.75
30.25 + -11h + h2 = 30.75

Factor a perfect square on the left side:
(h + -5.5)(h + -5.5) = 30.75

Calculate the square root of the right side: 5.545268253

Break this problem into two subproblems by setting 
(h + -5.5) equal to 5.545268253 and -5.545268253.

Subproblem 1
h + -5.5 = 5.545268253

Simplifying
h + -5.5 = 5.545268253

Reorder the terms:
-5.5 + h = 5.545268253

Solving
-5.5 + h = 5.545268253

Solving for variable 'h'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + h = 5.545268253 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + h = 5.545268253 + 5.5
h = 5.545268253 + 5.5

Combine like terms: 5.545268253 + 5.5 = 11.045268253
h = 11.045268253

Simplifying
h = 11.045268253

Subproblem 2
h + -5.5 = -5.545268253

Simplifying
h + -5.5 = -5.545268253

Reorder the terms:
-5.5 + h = -5.545268253

Solving
-5.5 + h = -5.545268253

Solving for variable 'h'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + h = -5.545268253 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + h = -5.545268253 + 5.5
h = -5.545268253 + 5.5

Combine like terms: -5.545268253 + 5.5 = -0.045268253
h = -0.045268253

Simplifying
h = -0.045268253

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {11.045268253, -0.045268253}
Solution
h = {11.045268253, -0.045268253}