-9-9h^2+18+18h=0

Solution for -9-9h^2+18+18h=0 equation:

Simplifying
-9 + -9h2 + 18 + 18h = 0

Reorder the terms:
-9 + 18 + 18h + -9h2 = 0

Combine like terms: -9 + 18 = 9
9 + 18h + -9h2 = 0

Solving
9 + 18h + -9h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '9'.
9(1 + 2h + -1h2) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(1 + 2h + -1h2)' equal to zero and attempt to solve:

Simplifying
1 + 2h + -1h2 = 0

Solving
1 + 2h + -1h2 = 0

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

Divide each side by '-1'.
-1 + -2h + h2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -2h + 1 + h2 = 0 + 1

Reorder the terms:
-1 + 1 + -2h + h2 = 0 + 1

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

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

The h term is -2h.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2h + 1 + h2 = 1 + 1

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

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

Factor a perfect square on the left side:
(h + -1)(h + -1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(h + -1) equal to 1.414213562 and -1.414213562.

Subproblem 1
h + -1 = 1.414213562

Simplifying
h + -1 = 1.414213562

Reorder the terms:
-1 + h = 1.414213562

Solving
-1 + h = 1.414213562

Solving for variable 'h'.

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

Add '1' to each side of the equation.
-1 + 1 + h = 1.414213562 + 1

Combine like terms: -1 + 1 = 0
0 + h = 1.414213562 + 1
h = 1.414213562 + 1

Combine like terms: 1.414213562 + 1 = 2.414213562
h = 2.414213562

Simplifying
h = 2.414213562

Subproblem 2
h + -1 = -1.414213562

Simplifying
h + -1 = -1.414213562

Reorder the terms:
-1 + h = -1.414213562

Solving
-1 + h = -1.414213562

Solving for variable 'h'.

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

Add '1' to each side of the equation.
-1 + 1 + h = -1.414213562 + 1

Combine like terms: -1 + 1 = 0
0 + h = -1.414213562 + 1
h = -1.414213562 + 1

Combine like terms: -1.414213562 + 1 = -0.414213562
h = -0.414213562

Simplifying
h = -0.414213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {2.414213562, -0.414213562}
Solution
h = {2.414213562, -0.414213562}