(2w)(w-2)=112

Solution for (2w)(w-2)=112 equation:

Simplifying
(2w)(w + -2) = 112

Remove parenthesis around (2w)
2w(w + -2) = 112

Reorder the terms:
2w(-2 + w) = 112
(-2 * 2w + w * 2w) = 112
(-4w + 2w2) = 112

Solving
-4w + 2w2 = 112

Solving for variable 'w'.

Reorder the terms:
-112 + -4w + 2w2 = 112 + -112

Combine like terms: 112 + -112 = 0
-112 + -4w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-56 + -2w + w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-56 + -2w + w2)' equal to zero and attempt to solve:

Simplifying
-56 + -2w + w2 = 0

Solving
-56 + -2w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '56' to each side of the equation.
-56 + -2w + 56 + w2 = 0 + 56

Reorder the terms:
-56 + 56 + -2w + w2 = 0 + 56

Combine like terms: -56 + 56 = 0
0 + -2w + w2 = 0 + 56
-2w + w2 = 0 + 56

Combine like terms: 0 + 56 = 56
-2w + w2 = 56

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 = 56 + 1

Reorder the terms:
1 + -2w + w2 = 56 + 1

Combine like terms: 56 + 1 = 57
1 + -2w + w2 = 57

Factor a perfect square on the left side:
(w + -1)(w + -1) = 57

Calculate the square root of the right side: 7.549834435

Break this problem into two subproblems by setting 
(w + -1) equal to 7.549834435 and -7.549834435.

Subproblem 1
w + -1 = 7.549834435

Simplifying
w + -1 = 7.549834435

Reorder the terms:
-1 + w = 7.549834435

Solving
-1 + w = 7.549834435

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 = 7.549834435 + 1

Combine like terms: -1 + 1 = 0
0 + w = 7.549834435 + 1
w = 7.549834435 + 1

Combine like terms: 7.549834435 + 1 = 8.549834435
w = 8.549834435

Simplifying
w = 8.549834435

Subproblem 2
w + -1 = -7.549834435

Simplifying
w + -1 = -7.549834435

Reorder the terms:
-1 + w = -7.549834435

Solving
-1 + w = -7.549834435

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 = -7.549834435 + 1

Combine like terms: -1 + 1 = 0
0 + w = -7.549834435 + 1
w = -7.549834435 + 1

Combine like terms: -7.549834435 + 1 = -6.549834435
w = -6.549834435

Simplifying
w = -6.549834435

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {8.549834435, -6.549834435}
Solution
w = {8.549834435, -6.549834435}