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 = -10h
3(-6 + -10h + 4h2) = 9
(-6 * 3 + -10h * 3 + 4h2 * 3) = 9
(-18 + -30h + 12h2) = 9

Solving
-18 + -30h + 12h2 = 9

Solving for variable 'h'.

Reorder the terms:
-18 + -9 + -30h + 12h2 = 9 + -9

Combine like terms: -18 + -9 = -27
-27 + -30h + 12h2 = 9 + -9

Combine like terms: 9 + -9 = 0
-27 + -30h + 12h2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + -10h + 4h2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-9 + -10h + 4h2)' equal to zero and attempt to solve:

Simplifying
-9 + -10h + 4h2 = 0

Solving
-9 + -10h + 4h2 = 0

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

Divide each side by '4'.
-2.25 + -2.5h + h2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + -2.5h + 2.25 + h2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + -2.5h + h2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + -2.5h + h2 = 0 + 2.25
-2.5h + h2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
-2.5h + h2 = 2.25

The h term is -2.5h.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5h + 1.5625 + h2 = 2.25 + 1.5625

Reorder the terms:
1.5625 + -2.5h + h2 = 2.25 + 1.5625

Combine like terms: 2.25 + 1.5625 = 3.8125
1.5625 + -2.5h + h2 = 3.8125

Factor a perfect square on the left side:
(h + -1.25)(h + -1.25) = 3.8125

Calculate the square root of the right side: 1.952562419

Break this problem into two subproblems by setting 
(h + -1.25) equal to 1.952562419 and -1.952562419.

Subproblem 1
h + -1.25 = 1.952562419

Simplifying
h + -1.25 = 1.952562419

Reorder the terms:
-1.25 + h = 1.952562419

Solving
-1.25 + h = 1.952562419

Solving for variable 'h'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + h = 1.952562419 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + h = 1.952562419 + 1.25
h = 1.952562419 + 1.25

Combine like terms: 1.952562419 + 1.25 = 3.202562419
h = 3.202562419

Simplifying
h = 3.202562419

Subproblem 2
h + -1.25 = -1.952562419

Simplifying
h + -1.25 = -1.952562419

Reorder the terms:
-1.25 + h = -1.952562419

Solving
-1.25 + h = -1.952562419

Solving for variable 'h'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + h = -1.952562419 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + h = -1.952562419 + 1.25
h = -1.952562419 + 1.25

Combine like terms: -1.952562419 + 1.25 = -0.702562419
h = -0.702562419

Simplifying
h = -0.702562419

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {3.202562419, -0.702562419}
Solution
h = {3.202562419, -0.702562419}