86=(4w-2)w

Solution for 86=(4w-2)w equation:

Simplifying
86 = (4w + -2) * w

Reorder the terms:
86 = (-2 + 4w) * w

Reorder the terms for easier multiplication:
86 = w(-2 + 4w)
86 = (-2 * w + 4w * w)
86 = (-2w + 4w2)

Solving
86 = -2w + 4w2

Solving for variable 'w'.

Reorder the terms:
86 + 2w + -4w2 = -2w + 2w + 4w2 + -4w2

Combine like terms: -2w + 2w = 0
86 + 2w + -4w2 = 0 + 4w2 + -4w2
86 + 2w + -4w2 = 4w2 + -4w2

Combine like terms: 4w2 + -4w2 = 0
86 + 2w + -4w2 = 0

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

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

Simplifying
43 + w + -2w2 = 0

Solving
43 + w + -2w2 = 0

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

Divide each side by '-2'.
-21.5 + -0.5w + w2 = 0

Move the constant term to the right:

Add '21.5' to each side of the equation.
-21.5 + -0.5w + 21.5 + w2 = 0 + 21.5

Reorder the terms:
-21.5 + 21.5 + -0.5w + w2 = 0 + 21.5

Combine like terms: -21.5 + 21.5 = 0.0
0.0 + -0.5w + w2 = 0 + 21.5
-0.5w + w2 = 0 + 21.5

Combine like terms: 0 + 21.5 = 21.5
-0.5w + w2 = 21.5

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

Add '0.25' to each side of the equation.
-0.5w + 0.25 + w2 = 21.5 + 0.25

Reorder the terms:
0.25 + -0.5w + w2 = 21.5 + 0.25

Combine like terms: 21.5 + 0.25 = 21.75
0.25 + -0.5w + w2 = 21.75

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = 21.75

Calculate the square root of the right side: 4.663689527

Break this problem into two subproblems by setting 
(w + 0.5) equal to 4.663689527 and -4.663689527.

Subproblem 1
w + 0.5 = 4.663689527

Simplifying
w + 0.5 = 4.663689527

Reorder the terms:
0.5 + w = 4.663689527

Solving
0.5 + w = 4.663689527

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = 4.663689527 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = 4.663689527 + -0.5
w = 4.663689527 + -0.5

Combine like terms: 4.663689527 + -0.5 = 4.163689527
w = 4.163689527

Simplifying
w = 4.163689527

Subproblem 2
w + 0.5 = -4.663689527

Simplifying
w + 0.5 = -4.663689527

Reorder the terms:
0.5 + w = -4.663689527

Solving
0.5 + w = -4.663689527

Solving for variable 'w'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + w = -4.663689527 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = -4.663689527 + -0.5
w = -4.663689527 + -0.5

Combine like terms: -4.663689527 + -0.5 = -5.163689527
w = -5.163689527

Simplifying
w = -5.163689527

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {4.163689527, -5.163689527}
Solution
w = {4.163689527, -5.163689527}