3(2h-6)(-2h+1)=9

Solution for 3(2h-6)(-2h+1)=9 equation:

Simplifying
3(2h + -6)(-2h + 1) = 9

Reorder the terms:
3(-6 + 2h)(-2h + 1) = 9

Reorder the terms:
3(-6 + 2h)(1 + -2h) = 9

Multiply (-6 + 2h) * (1 + -2h)
3(-6(1 + -2h) + 2h * (1 + -2h)) = 9
3((1 * -6 + -2h * -6) + 2h * (1 + -2h)) = 9
3((-6 + 12h) + 2h * (1 + -2h)) = 9
3(-6 + 12h + (1 * 2h + -2h * 2h)) = 9
3(-6 + 12h + (2h + -4h2)) = 9

Combine like terms: 12h + 2h = 14h
3(-6 + 14h + -4h2) = 9
(-6 * 3 + 14h * 3 + -4h2 * 3) = 9
(-18 + 42h + -12h2) = 9

Solving
-18 + 42h + -12h2 = 9

Solving for variable 'h'.

Reorder the terms:
-18 + -9 + 42h + -12h2 = 9 + -9

Combine like terms: -18 + -9 = -27
-27 + 42h + -12h2 = 9 + -9

Combine like terms: 9 + -9 = 0
-27 + 42h + -12h2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + 14h + -4h2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-9 + 14h + -4h2)' equal to zero and attempt to solve:

Simplifying
-9 + 14h + -4h2 = 0

Solving
-9 + 14h + -4h2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
2.25 + -3.5h + h2 = 0

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + -3.5h + -2.25 + h2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + -3.5h + h2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + -3.5h + h2 = 0 + -2.25
-3.5h + h2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
-3.5h + h2 = -2.25

The h term is -3.5h.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5h + 3.0625 + h2 = -2.25 + 3.0625

Reorder the terms:
3.0625 + -3.5h + h2 = -2.25 + 3.0625

Combine like terms: -2.25 + 3.0625 = 0.8125
3.0625 + -3.5h + h2 = 0.8125

Factor a perfect square on the left side:
(h + -1.75)(h + -1.75) = 0.8125

Calculate the square root of the right side: 0.901387819

Break this problem into two subproblems by setting 
(h + -1.75) equal to 0.901387819 and -0.901387819.

Subproblem 1
h + -1.75 = 0.901387819

Simplifying
h + -1.75 = 0.901387819

Reorder the terms:
-1.75 + h = 0.901387819

Solving
-1.75 + h = 0.901387819

Solving for variable 'h'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + h = 0.901387819 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + h = 0.901387819 + 1.75
h = 0.901387819 + 1.75

Combine like terms: 0.901387819 + 1.75 = 2.651387819
h = 2.651387819

Simplifying
h = 2.651387819

Subproblem 2
h + -1.75 = -0.901387819

Simplifying
h + -1.75 = -0.901387819

Reorder the terms:
-1.75 + h = -0.901387819

Solving
-1.75 + h = -0.901387819

Solving for variable 'h'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + h = -0.901387819 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + h = -0.901387819 + 1.75
h = -0.901387819 + 1.75

Combine like terms: -0.901387819 + 1.75 = 0.848612181
h = 0.848612181

Simplifying
h = 0.848612181

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {2.651387819, 0.848612181}
Solution
h = {2.651387819, 0.848612181}