26=6(w+7)2w

Solution for 26=6(w+7)2w equation:

Simplifying
26 = 6(w + 7) * 2w

Reorder the terms:
26 = 6(7 + w) * 2w

Reorder the terms for easier multiplication:
26 = 6 * 2w(7 + w)

Multiply 6 * 2
26 = 12w(7 + w)
26 = (7 * 12w + w * 12w)
26 = (84w + 12w2)

Solving
26 = 84w + 12w2

Solving for variable 'w'.

Reorder the terms:
26 + -84w + -12w2 = 84w + -84w + 12w2 + -12w2

Combine like terms: 84w + -84w = 0
26 + -84w + -12w2 = 0 + 12w2 + -12w2
26 + -84w + -12w2 = 12w2 + -12w2

Combine like terms: 12w2 + -12w2 = 0
26 + -84w + -12w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(13 + -42w + -6w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(13 + -42w + -6w2)' equal to zero and attempt to solve:

Simplifying
13 + -42w + -6w2 = 0

Solving
13 + -42w + -6w2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-2.166666667 + 7w + w2 = 0

Move the constant term to the right:

Add '2.166666667' to each side of the equation.
-2.166666667 + 7w + 2.166666667 + w2 = 0 + 2.166666667

Reorder the terms:
-2.166666667 + 2.166666667 + 7w + w2 = 0 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + 7w + w2 = 0 + 2.166666667
7w + w2 = 0 + 2.166666667

Combine like terms: 0 + 2.166666667 = 2.166666667
7w + w2 = 2.166666667

The w term is 7w.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7w + 12.25 + w2 = 2.166666667 + 12.25

Reorder the terms:
12.25 + 7w + w2 = 2.166666667 + 12.25

Combine like terms: 2.166666667 + 12.25 = 14.416666667
12.25 + 7w + w2 = 14.416666667

Factor a perfect square on the left side:
(w + 3.5)(w + 3.5) = 14.416666667

Calculate the square root of the right side: 3.796928583

Break this problem into two subproblems by setting 
(w + 3.5) equal to 3.796928583 and -3.796928583.

Subproblem 1
w + 3.5 = 3.796928583

Simplifying
w + 3.5 = 3.796928583

Reorder the terms:
3.5 + w = 3.796928583

Solving
3.5 + w = 3.796928583

Solving for variable 'w'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + w = 3.796928583 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + w = 3.796928583 + -3.5
w = 3.796928583 + -3.5

Combine like terms: 3.796928583 + -3.5 = 0.296928583
w = 0.296928583

Simplifying
w = 0.296928583

Subproblem 2
w + 3.5 = -3.796928583

Simplifying
w + 3.5 = -3.796928583

Reorder the terms:
3.5 + w = -3.796928583

Solving
3.5 + w = -3.796928583

Solving for variable 'w'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + w = -3.796928583 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + w = -3.796928583 + -3.5
w = -3.796928583 + -3.5

Combine like terms: -3.796928583 + -3.5 = -7.296928583
w = -7.296928583

Simplifying
w = -7.296928583

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {0.296928583, -7.296928583}
Solution
w = {0.296928583, -7.296928583}