86=2(w*(w+13))

Solution for 86=2(w*(w+13)) equation:

Simplifying
86 = 2(w(w + 13))

Reorder the terms:
86 = 2(w(13 + w))
86 = 2((13 * w + w * w))
86 = 2((13w + w2))
86 = (13w * 2 + w2 * 2)
86 = (26w + 2w2)

Solving
86 = 26w + 2w2

Solving for variable 'w'.

Reorder the terms:
86 + -26w + -2w2 = 26w + -26w + 2w2 + -2w2

Combine like terms: 26w + -26w = 0
86 + -26w + -2w2 = 0 + 2w2 + -2w2
86 + -26w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
86 + -26w + -2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(43 + -13w + -1w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(43 + -13w + -1w2)' equal to zero and attempt to solve:

Simplifying
43 + -13w + -1w2 = 0

Solving
43 + -13w + -1w2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-43 + 13w + w2 = 0

Move the constant term to the right:

Add '43' to each side of the equation.
-43 + 13w + 43 + w2 = 0 + 43

Reorder the terms:
-43 + 43 + 13w + w2 = 0 + 43

Combine like terms: -43 + 43 = 0
0 + 13w + w2 = 0 + 43
13w + w2 = 0 + 43

Combine like terms: 0 + 43 = 43
13w + w2 = 43

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 = 43 + 42.25

Reorder the terms:
42.25 + 13w + w2 = 43 + 42.25

Combine like terms: 43 + 42.25 = 85.25
42.25 + 13w + w2 = 85.25

Factor a perfect square on the left side:
(w + 6.5)(w + 6.5) = 85.25

Calculate the square root of the right side: 9.233092656

Break this problem into two subproblems by setting 
(w + 6.5) equal to 9.233092656 and -9.233092656.

Subproblem 1
w + 6.5 = 9.233092656

Simplifying
w + 6.5 = 9.233092656

Reorder the terms:
6.5 + w = 9.233092656

Solving
6.5 + w = 9.233092656

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 = 9.233092656 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + w = 9.233092656 + -6.5
w = 9.233092656 + -6.5

Combine like terms: 9.233092656 + -6.5 = 2.733092656
w = 2.733092656

Simplifying
w = 2.733092656

Subproblem 2
w + 6.5 = -9.233092656

Simplifying
w + 6.5 = -9.233092656

Reorder the terms:
6.5 + w = -9.233092656

Solving
6.5 + w = -9.233092656

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 = -9.233092656 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + w = -9.233092656 + -6.5
w = -9.233092656 + -6.5

Combine like terms: -9.233092656 + -6.5 = -15.733092656
w = -15.733092656

Simplifying
w = -15.733092656

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {2.733092656, -15.733092656}
Solution
w = {2.733092656, -15.733092656}