-9h+6(6+4h)h=6

Solution for -9h+6(6+4h)h=6 equation:

Simplifying
-9h + 6(6 + 4h) * h = 6

Reorder the terms for easier multiplication:
-9h + 6h(6 + 4h) = 6
-9h + (6 * 6h + 4h * 6h) = 6
-9h + (36h + 24h2) = 6

Combine like terms: -9h + 36h = 27h
27h + 24h2 = 6

Solving
27h + 24h2 = 6

Solving for variable 'h'.

Reorder the terms:
-6 + 27h + 24h2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 27h + 24h2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 9h + 8h2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + 9h + 8h2)' equal to zero and attempt to solve:

Simplifying
-2 + 9h + 8h2 = 0

Solving
-2 + 9h + 8h2 = 0

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

Divide each side by '8'.
-0.25 + 1.125h + h2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 1.125h + 0.25 + h2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 1.125h + h2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 1.125h + h2 = 0 + 0.25
1.125h + h2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
1.125h + h2 = 0.25

The h term is 1.125h.  Take half its coefficient (0.5625).
Square it (0.31640625) and add it to both sides.

Add '0.31640625' to each side of the equation.
1.125h + 0.31640625 + h2 = 0.25 + 0.31640625

Reorder the terms:
0.31640625 + 1.125h + h2 = 0.25 + 0.31640625

Combine like terms: 0.25 + 0.31640625 = 0.56640625
0.31640625 + 1.125h + h2 = 0.56640625

Factor a perfect square on the left side:
(h + 0.5625)(h + 0.5625) = 0.56640625

Calculate the square root of the right side: 0.752599661

Break this problem into two subproblems by setting 
(h + 0.5625) equal to 0.752599661 and -0.752599661.

Subproblem 1
h + 0.5625 = 0.752599661

Simplifying
h + 0.5625 = 0.752599661

Reorder the terms:
0.5625 + h = 0.752599661

Solving
0.5625 + h = 0.752599661

Solving for variable 'h'.

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

Add '-0.5625' to each side of the equation.
0.5625 + -0.5625 + h = 0.752599661 + -0.5625

Combine like terms: 0.5625 + -0.5625 = 0.0000
0.0000 + h = 0.752599661 + -0.5625
h = 0.752599661 + -0.5625

Combine like terms: 0.752599661 + -0.5625 = 0.190099661
h = 0.190099661

Simplifying
h = 0.190099661

Subproblem 2
h + 0.5625 = -0.752599661

Simplifying
h + 0.5625 = -0.752599661

Reorder the terms:
0.5625 + h = -0.752599661

Solving
0.5625 + h = -0.752599661

Solving for variable 'h'.

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

Add '-0.5625' to each side of the equation.
0.5625 + -0.5625 + h = -0.752599661 + -0.5625

Combine like terms: 0.5625 + -0.5625 = 0.0000
0.0000 + h = -0.752599661 + -0.5625
h = -0.752599661 + -0.5625

Combine like terms: -0.752599661 + -0.5625 = -1.315099661
h = -1.315099661

Simplifying
h = -1.315099661

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {0.190099661, -1.315099661}
Solution
h = {0.190099661, -1.315099661}