72=2(w+6)(2w)

Solution for 72=2(w+6)(2w) equation:

Simplifying
72 = 2(w + 6)(2w)

Reorder the terms:
72 = 2(6 + w)(2w)

Remove parenthesis around (2w)
72 = 2(6 + w) * 2w

Reorder the terms for easier multiplication:
72 = 2 * 2w(6 + w)

Multiply 2 * 2
72 = 4w(6 + w)
72 = (6 * 4w + w * 4w)
72 = (24w + 4w2)

Solving
72 = 24w + 4w2

Solving for variable 'w'.

Reorder the terms:
72 + -24w + -4w2 = 24w + -24w + 4w2 + -4w2

Combine like terms: 24w + -24w = 0
72 + -24w + -4w2 = 0 + 4w2 + -4w2
72 + -24w + -4w2 = 4w2 + -4w2

Combine like terms: 4w2 + -4w2 = 0
72 + -24w + -4w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(18 + -6w + -1w2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(18 + -6w + -1w2)' equal to zero and attempt to solve:

Simplifying
18 + -6w + -1w2 = 0

Solving
18 + -6w + -1w2 = 0

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

Divide each side by '-1'.
-18 + 6w + w2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 6w + 18 + w2 = 0 + 18

Reorder the terms:
-18 + 18 + 6w + w2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 6w + w2 = 0 + 18
6w + w2 = 0 + 18

Combine like terms: 0 + 18 = 18
6w + w2 = 18

The w term is 6w.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6w + 9 + w2 = 18 + 9

Reorder the terms:
9 + 6w + w2 = 18 + 9

Combine like terms: 18 + 9 = 27
9 + 6w + w2 = 27

Factor a perfect square on the left side:
(w + 3)(w + 3) = 27

Calculate the square root of the right side: 5.196152423

Break this problem into two subproblems by setting 
(w + 3) equal to 5.196152423 and -5.196152423.

Subproblem 1
w + 3 = 5.196152423

Simplifying
w + 3 = 5.196152423

Reorder the terms:
3 + w = 5.196152423

Solving
3 + w = 5.196152423

Solving for variable 'w'.

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

Add '-3' to each side of the equation.
3 + -3 + w = 5.196152423 + -3

Combine like terms: 3 + -3 = 0
0 + w = 5.196152423 + -3
w = 5.196152423 + -3

Combine like terms: 5.196152423 + -3 = 2.196152423
w = 2.196152423

Simplifying
w = 2.196152423

Subproblem 2
w + 3 = -5.196152423

Simplifying
w + 3 = -5.196152423

Reorder the terms:
3 + w = -5.196152423

Solving
3 + w = -5.196152423

Solving for variable 'w'.

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

Add '-3' to each side of the equation.
3 + -3 + w = -5.196152423 + -3

Combine like terms: 3 + -3 = 0
0 + w = -5.196152423 + -3
w = -5.196152423 + -3

Combine like terms: -5.196152423 + -3 = -8.196152423
w = -8.196152423

Simplifying
w = -8.196152423

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {2.196152423, -8.196152423}
Solution
w = {2.196152423, -8.196152423}