92=2((2w+1)(w))

Solution for 92=2((2w+1)(w)) equation:

Simplifying
92 = 2((2w + 1)(w))

Reorder the terms:
92 = 2((1 + 2w)(w))

Reorder the terms for easier multiplication:
92 = 2(w(1 + 2w))
92 = 2((1 * w + 2w * w))
92 = 2((1w + 2w2))
92 = (1w * 2 + 2w2 * 2)
92 = (2w + 4w2)

Solving
92 = 2w + 4w2

Solving for variable 'w'.

Reorder the terms:
92 + -2w + -4w2 = 2w + -2w + 4w2 + -4w2

Combine like terms: 2w + -2w = 0
92 + -2w + -4w2 = 0 + 4w2 + -4w2
92 + -2w + -4w2 = 4w2 + -4w2

Combine like terms: 4w2 + -4w2 = 0
92 + -2w + -4w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(46 + -1w + -2w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(46 + -1w + -2w2)' equal to zero and attempt to solve:

Simplifying
46 + -1w + -2w2 = 0

Solving
46 + -1w + -2w2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-23 + 0.5w + w2 = 0

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + 0.5w + 23 + w2 = 0 + 23

Reorder the terms:
-23 + 23 + 0.5w + w2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + 0.5w + w2 = 0 + 23
0.5w + w2 = 0 + 23

Combine like terms: 0 + 23 = 23
0.5w + w2 = 23

The w term is 0.5w.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5w + 0.0625 + w2 = 23 + 0.0625

Reorder the terms:
0.0625 + 0.5w + w2 = 23 + 0.0625

Combine like terms: 23 + 0.0625 = 23.0625
0.0625 + 0.5w + w2 = 23.0625

Factor a perfect square on the left side:
(w + 0.25)(w + 0.25) = 23.0625

Calculate the square root of the right side: 4.802343178

Break this problem into two subproblems by setting 
(w + 0.25) equal to 4.802343178 and -4.802343178.

Subproblem 1
w + 0.25 = 4.802343178

Simplifying
w + 0.25 = 4.802343178

Reorder the terms:
0.25 + w = 4.802343178

Solving
0.25 + w = 4.802343178

Solving for variable 'w'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + w = 4.802343178 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + w = 4.802343178 + -0.25
w = 4.802343178 + -0.25

Combine like terms: 4.802343178 + -0.25 = 4.552343178
w = 4.552343178

Simplifying
w = 4.552343178

Subproblem 2
w + 0.25 = -4.802343178

Simplifying
w + 0.25 = -4.802343178

Reorder the terms:
0.25 + w = -4.802343178

Solving
0.25 + w = -4.802343178

Solving for variable 'w'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + w = -4.802343178 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + w = -4.802343178 + -0.25
w = -4.802343178 + -0.25

Combine like terms: -4.802343178 + -0.25 = -5.052343178
w = -5.052343178

Simplifying
w = -5.052343178

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.552343178, -5.052343178}
Solution
w = {4.552343178, -5.052343178}