2(2h+3)*2h=27

Solution for 2(2h+3)*2h=27 equation:

Simplifying
2(2h + 3) * 2h = 27

Reorder the terms:
2(3 + 2h) * 2h = 27

Reorder the terms for easier multiplication:
2 * 2h(3 + 2h) = 27

Multiply 2 * 2
4h(3 + 2h) = 27
(3 * 4h + 2h * 4h) = 27
(12h + 8h2) = 27

Solving
12h + 8h2 = 27

Solving for variable 'h'.

Reorder the terms:
-27 + 12h + 8h2 = 27 + -27

Combine like terms: 27 + -27 = 0
-27 + 12h + 8h2 = 0

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

Divide each side by '8'.
-3.375 + 1.5h + h2 = 0

Move the constant term to the right:

Add '3.375' to each side of the equation.
-3.375 + 1.5h + 3.375 + h2 = 0 + 3.375

Reorder the terms:
-3.375 + 3.375 + 1.5h + h2 = 0 + 3.375

Combine like terms: -3.375 + 3.375 = 0.000
0.000 + 1.5h + h2 = 0 + 3.375
1.5h + h2 = 0 + 3.375

Combine like terms: 0 + 3.375 = 3.375
1.5h + h2 = 3.375

The h term is 1.5h.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5h + 0.5625 + h2 = 3.375 + 0.5625

Reorder the terms:
0.5625 + 1.5h + h2 = 3.375 + 0.5625

Combine like terms: 3.375 + 0.5625 = 3.9375
0.5625 + 1.5h + h2 = 3.9375

Factor a perfect square on the left side:
(h + 0.75)(h + 0.75) = 3.9375

Calculate the square root of the right side: 1.984313483

Break this problem into two subproblems by setting 
(h + 0.75) equal to 1.984313483 and -1.984313483.

Subproblem 1
h + 0.75 = 1.984313483

Simplifying
h + 0.75 = 1.984313483

Reorder the terms:
0.75 + h = 1.984313483

Solving
0.75 + h = 1.984313483

Solving for variable 'h'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + h = 1.984313483 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + h = 1.984313483 + -0.75
h = 1.984313483 + -0.75

Combine like terms: 1.984313483 + -0.75 = 1.234313483
h = 1.234313483

Simplifying
h = 1.234313483

Subproblem 2
h + 0.75 = -1.984313483

Simplifying
h + 0.75 = -1.984313483

Reorder the terms:
0.75 + h = -1.984313483

Solving
0.75 + h = -1.984313483

Solving for variable 'h'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + h = -1.984313483 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + h = -1.984313483 + -0.75
h = -1.984313483 + -0.75

Combine like terms: -1.984313483 + -0.75 = -2.734313483
h = -2.734313483

Simplifying
h = -2.734313483

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {1.234313483, -2.734313483}