(2w-2)(w-2)=32

Solution for (2w-2)(w-2)=32 equation:

Simplifying
(2w + -2)(w + -2) = 32

Reorder the terms:
(-2 + 2w)(w + -2) = 32

Reorder the terms:
(-2 + 2w)(-2 + w) = 32

Multiply (-2 + 2w) * (-2 + w)
(-2(-2 + w) + 2w * (-2 + w)) = 32
((-2 * -2 + w * -2) + 2w * (-2 + w)) = 32
((4 + -2w) + 2w * (-2 + w)) = 32
(4 + -2w + (-2 * 2w + w * 2w)) = 32
(4 + -2w + (-4w + 2w2)) = 32

Combine like terms: -2w + -4w = -6w
(4 + -6w + 2w2) = 32

Solving
4 + -6w + 2w2 = 32

Solving for variable 'w'.

Reorder the terms:
4 + -32 + -6w + 2w2 = 32 + -32

Combine like terms: 4 + -32 = -28
-28 + -6w + 2w2 = 32 + -32

Combine like terms: 32 + -32 = 0
-28 + -6w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + -3w + w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-14 + -3w + w2)' equal to zero and attempt to solve:

Simplifying
-14 + -3w + w2 = 0

Solving
-14 + -3w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -3w + 14 + w2 = 0 + 14

Reorder the terms:
-14 + 14 + -3w + w2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -3w + w2 = 0 + 14
-3w + w2 = 0 + 14

Combine like terms: 0 + 14 = 14
-3w + w2 = 14

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 = 14 + 2.25

Reorder the terms:
2.25 + -3w + w2 = 14 + 2.25

Combine like terms: 14 + 2.25 = 16.25
2.25 + -3w + w2 = 16.25

Factor a perfect square on the left side:
(w + -1.5)(w + -1.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(w + -1.5) equal to 4.031128874 and -4.031128874.

Subproblem 1
w + -1.5 = 4.031128874

Simplifying
w + -1.5 = 4.031128874

Reorder the terms:
-1.5 + w = 4.031128874

Solving
-1.5 + w = 4.031128874

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 = 4.031128874 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + w = 4.031128874 + 1.5
w = 4.031128874 + 1.5

Combine like terms: 4.031128874 + 1.5 = 5.531128874
w = 5.531128874

Simplifying
w = 5.531128874

Subproblem 2
w + -1.5 = -4.031128874

Simplifying
w + -1.5 = -4.031128874

Reorder the terms:
-1.5 + w = -4.031128874

Solving
-1.5 + w = -4.031128874

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 = -4.031128874 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + w = -4.031128874 + 1.5
w = -4.031128874 + 1.5

Combine like terms: -4.031128874 + 1.5 = -2.531128874
w = -2.531128874

Simplifying
w = -2.531128874

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {5.531128874, -2.531128874}
Solution
w = {5.531128874, -2.531128874}