2w(w-2)=54

Solution for 2w(w-2)=54 equation:

Simplifying
2w(w + -2) = 54

Reorder the terms:
2w(-2 + w) = 54
(-2 * 2w + w * 2w) = 54
(-4w + 2w2) = 54

Solving
-4w + 2w2 = 54

Solving for variable 'w'.

Reorder the terms:
-54 + -4w + 2w2 = 54 + -54

Combine like terms: 54 + -54 = 0
-54 + -4w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + -2w + w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-27 + -2w + w2)' equal to zero and attempt to solve:

Simplifying
-27 + -2w + w2 = 0

Solving
-27 + -2w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + -2w + 27 + w2 = 0 + 27

Reorder the terms:
-27 + 27 + -2w + w2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -2w + w2 = 0 + 27
-2w + w2 = 0 + 27

Combine like terms: 0 + 27 = 27
-2w + w2 = 27

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 = 27 + 1

Reorder the terms:
1 + -2w + w2 = 27 + 1

Combine like terms: 27 + 1 = 28
1 + -2w + w2 = 28

Factor a perfect square on the left side:
(w + -1)(w + -1) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(w + -1) equal to 5.291502622 and -5.291502622.

Subproblem 1
w + -1 = 5.291502622

Simplifying
w + -1 = 5.291502622

Reorder the terms:
-1 + w = 5.291502622

Solving
-1 + w = 5.291502622

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 = 5.291502622 + 1

Combine like terms: -1 + 1 = 0
0 + w = 5.291502622 + 1
w = 5.291502622 + 1

Combine like terms: 5.291502622 + 1 = 6.291502622
w = 6.291502622

Simplifying
w = 6.291502622

Subproblem 2
w + -1 = -5.291502622

Simplifying
w + -1 = -5.291502622

Reorder the terms:
-1 + w = -5.291502622

Solving
-1 + w = -5.291502622

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 = -5.291502622 + 1

Combine like terms: -1 + 1 = 0
0 + w = -5.291502622 + 1
w = -5.291502622 + 1

Combine like terms: -5.291502622 + 1 = -4.291502622
w = -4.291502622

Simplifying
w = -4.291502622

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {6.291502622, -4.291502622}
Solution
w = {6.291502622, -4.291502622}