2w*2(2w+6)=226

Solution for 2w*2(2w+6)=226 equation:

Simplifying
2w * 2(2w + 6) = 226

Reorder the terms:
2w * 2(6 + 2w) = 226

Reorder the terms for easier multiplication:
2 * 2w(6 + 2w) = 226

Multiply 2 * 2
4w(6 + 2w) = 226
(6 * 4w + 2w * 4w) = 226
(24w + 8w2) = 226

Solving
24w + 8w2 = 226

Solving for variable 'w'.

Reorder the terms:
-226 + 24w + 8w2 = 226 + -226

Combine like terms: 226 + -226 = 0
-226 + 24w + 8w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-113 + 12w + 4w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-113 + 12w + 4w2)' equal to zero and attempt to solve:

Simplifying
-113 + 12w + 4w2 = 0

Solving
-113 + 12w + 4w2 = 0

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

Divide each side by '4'.
-28.25 + 3w + w2 = 0

Move the constant term to the right:

Add '28.25' to each side of the equation.
-28.25 + 3w + 28.25 + w2 = 0 + 28.25

Reorder the terms:
-28.25 + 28.25 + 3w + w2 = 0 + 28.25

Combine like terms: -28.25 + 28.25 = 0.00
0.00 + 3w + w2 = 0 + 28.25
3w + w2 = 0 + 28.25

Combine like terms: 0 + 28.25 = 28.25
3w + w2 = 28.25

The w term is 3w.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3w + 2.25 + w2 = 28.25 + 2.25

Reorder the terms:
2.25 + 3w + w2 = 28.25 + 2.25

Combine like terms: 28.25 + 2.25 = 30.5
2.25 + 3w + w2 = 30.5

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = 30.5

Calculate the square root of the right side: 5.522680509

Break this problem into two subproblems by setting 
(w + 1.5) equal to 5.522680509 and -5.522680509.

Subproblem 1
w + 1.5 = 5.522680509

Simplifying
w + 1.5 = 5.522680509

Reorder the terms:
1.5 + w = 5.522680509

Solving
1.5 + w = 5.522680509

Solving for variable 'w'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + w = 5.522680509 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = 5.522680509 + -1.5
w = 5.522680509 + -1.5

Combine like terms: 5.522680509 + -1.5 = 4.022680509
w = 4.022680509

Simplifying
w = 4.022680509

Subproblem 2
w + 1.5 = -5.522680509

Simplifying
w + 1.5 = -5.522680509

Reorder the terms:
1.5 + w = -5.522680509

Solving
1.5 + w = -5.522680509

Solving for variable 'w'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + w = -5.522680509 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = -5.522680509 + -1.5
w = -5.522680509 + -1.5

Combine like terms: -5.522680509 + -1.5 = -7.022680509
w = -7.022680509

Simplifying
w = -7.022680509

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.022680509, -7.022680509}
Solution
w = {4.022680509, -7.022680509}