(16+2w)(10+2w)=180

Solution for (16+2w)(10+2w)=180 equation:

Simplifying
(16 + 2w)(10 + 2w) = 180

Multiply (16 + 2w) * (10 + 2w)
(16(10 + 2w) + 2w * (10 + 2w)) = 180
((10 * 16 + 2w * 16) + 2w * (10 + 2w)) = 180
((160 + 32w) + 2w * (10 + 2w)) = 180
(160 + 32w + (10 * 2w + 2w * 2w)) = 180
(160 + 32w + (20w + 4w2)) = 180

Combine like terms: 32w + 20w = 52w
(160 + 52w + 4w2) = 180

Solving
160 + 52w + 4w2 = 180

Solving for variable 'w'.

Reorder the terms:
160 + -180 + 52w + 4w2 = 180 + -180

Combine like terms: 160 + -180 = -20
-20 + 52w + 4w2 = 180 + -180

Combine like terms: 180 + -180 = 0
-20 + 52w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + 13w + w2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-5 + 13w + w2)' equal to zero and attempt to solve:

Simplifying
-5 + 13w + w2 = 0

Solving
-5 + 13w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 13w + 5 + w2 = 0 + 5

Reorder the terms:
-5 + 5 + 13w + w2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 13w + w2 = 0 + 5
13w + w2 = 0 + 5

Combine like terms: 0 + 5 = 5
13w + w2 = 5

The w term is 13w.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13w + 42.25 + w2 = 5 + 42.25

Reorder the terms:
42.25 + 13w + w2 = 5 + 42.25

Combine like terms: 5 + 42.25 = 47.25
42.25 + 13w + w2 = 47.25

Factor a perfect square on the left side:
(w + 6.5)(w + 6.5) = 47.25

Calculate the square root of the right side: 6.873863542

Break this problem into two subproblems by setting 
(w + 6.5) equal to 6.873863542 and -6.873863542.

Subproblem 1
w + 6.5 = 6.873863542

Simplifying
w + 6.5 = 6.873863542

Reorder the terms:
6.5 + w = 6.873863542

Solving
6.5 + w = 6.873863542

Solving for variable 'w'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + w = 6.873863542 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + w = 6.873863542 + -6.5
w = 6.873863542 + -6.5

Combine like terms: 6.873863542 + -6.5 = 0.373863542
w = 0.373863542

Simplifying
w = 0.373863542

Subproblem 2
w + 6.5 = -6.873863542

Simplifying
w + 6.5 = -6.873863542

Reorder the terms:
6.5 + w = -6.873863542

Solving
6.5 + w = -6.873863542

Solving for variable 'w'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + w = -6.873863542 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + w = -6.873863542 + -6.5
w = -6.873863542 + -6.5

Combine like terms: -6.873863542 + -6.5 = -13.373863542
w = -13.373863542

Simplifying
w = -13.373863542

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.373863542, -13.373863542}
Solution
w = {0.373863542, -13.373863542}