(8w+8)(4w+4)=180

Solution for (8w+8)(4w+4)=180 equation:

Simplifying
(8w + 8)(4w + 4) = 180

Reorder the terms:
(8 + 8w)(4w + 4) = 180

Reorder the terms:
(8 + 8w)(4 + 4w) = 180

Multiply (8 + 8w) * (4 + 4w)
(8(4 + 4w) + 8w * (4 + 4w)) = 180
((4 * 8 + 4w * 8) + 8w * (4 + 4w)) = 180
((32 + 32w) + 8w * (4 + 4w)) = 180
(32 + 32w + (4 * 8w + 4w * 8w)) = 180
(32 + 32w + (32w + 32w2)) = 180

Combine like terms: 32w + 32w = 64w
(32 + 64w + 32w2) = 180

Solving
32 + 64w + 32w2 = 180

Solving for variable 'w'.

Reorder the terms:
32 + -180 + 64w + 32w2 = 180 + -180

Combine like terms: 32 + -180 = -148
-148 + 64w + 32w2 = 180 + -180

Combine like terms: 180 + -180 = 0
-148 + 64w + 32w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-37 + 16w + 8w2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-37 + 16w + 8w2)' equal to zero and attempt to solve:

Simplifying
-37 + 16w + 8w2 = 0

Solving
-37 + 16w + 8w2 = 0

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

Divide each side by '8'.
-4.625 + 2w + w2 = 0

Move the constant term to the right:

Add '4.625' to each side of the equation.
-4.625 + 2w + 4.625 + w2 = 0 + 4.625

Reorder the terms:
-4.625 + 4.625 + 2w + w2 = 0 + 4.625

Combine like terms: -4.625 + 4.625 = 0.000
0.000 + 2w + w2 = 0 + 4.625
2w + w2 = 0 + 4.625

Combine like terms: 0 + 4.625 = 4.625
2w + w2 = 4.625

The w term is 2w.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2w + 1 + w2 = 4.625 + 1

Reorder the terms:
1 + 2w + w2 = 4.625 + 1

Combine like terms: 4.625 + 1 = 5.625
1 + 2w + w2 = 5.625

Factor a perfect square on the left side:
(w + 1)(w + 1) = 5.625

Calculate the square root of the right side: 2.371708245

Break this problem into two subproblems by setting 
(w + 1) equal to 2.371708245 and -2.371708245.

Subproblem 1
w + 1 = 2.371708245

Simplifying
w + 1 = 2.371708245

Reorder the terms:
1 + w = 2.371708245

Solving
1 + w = 2.371708245

Solving for variable 'w'.

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

Add '-1' to each side of the equation.
1 + -1 + w = 2.371708245 + -1

Combine like terms: 1 + -1 = 0
0 + w = 2.371708245 + -1
w = 2.371708245 + -1

Combine like terms: 2.371708245 + -1 = 1.371708245
w = 1.371708245

Simplifying
w = 1.371708245

Subproblem 2
w + 1 = -2.371708245

Simplifying
w + 1 = -2.371708245

Reorder the terms:
1 + w = -2.371708245

Solving
1 + w = -2.371708245

Solving for variable 'w'.

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

Add '-1' to each side of the equation.
1 + -1 + w = -2.371708245 + -1

Combine like terms: 1 + -1 = 0
0 + w = -2.371708245 + -1
w = -2.371708245 + -1

Combine like terms: -2.371708245 + -1 = -3.371708245
w = -3.371708245

Simplifying
w = -3.371708245

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.371708245, -3.371708245}
Solution
w = {1.371708245, -3.371708245}