16w^2-40w+20=0

Solution for 16w^2-40w+20=0 equation:

Simplifying
16w2 + -40w + 20 = 0

Reorder the terms:
20 + -40w + 16w2 = 0

Solving
20 + -40w + 16w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + -10w + 4w2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(5 + -10w + 4w2)' equal to zero and attempt to solve:

Simplifying
5 + -10w + 4w2 = 0

Solving
5 + -10w + 4w2 = 0

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

Divide each side by '4'.
1.25 + -2.5w + w2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -2.5w + -1.25 + w2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -2.5w + w2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -2.5w + w2 = 0 + -1.25
-2.5w + w2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-2.5w + w2 = -1.25

The w term is -2.5w.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5w + 1.5625 + w2 = -1.25 + 1.5625

Reorder the terms:
1.5625 + -2.5w + w2 = -1.25 + 1.5625

Combine like terms: -1.25 + 1.5625 = 0.3125
1.5625 + -2.5w + w2 = 0.3125

Factor a perfect square on the left side:
(w + -1.25)(w + -1.25) = 0.3125

Calculate the square root of the right side: 0.559016994

Break this problem into two subproblems by setting 
(w + -1.25) equal to 0.559016994 and -0.559016994.

Subproblem 1
w + -1.25 = 0.559016994

Simplifying
w + -1.25 = 0.559016994

Reorder the terms:
-1.25 + w = 0.559016994

Solving
-1.25 + w = 0.559016994

Solving for variable 'w'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + w = 0.559016994 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + w = 0.559016994 + 1.25
w = 0.559016994 + 1.25

Combine like terms: 0.559016994 + 1.25 = 1.809016994
w = 1.809016994

Simplifying
w = 1.809016994

Subproblem 2
w + -1.25 = -0.559016994

Simplifying
w + -1.25 = -0.559016994

Reorder the terms:
-1.25 + w = -0.559016994

Solving
-1.25 + w = -0.559016994

Solving for variable 'w'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + w = -0.559016994 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + w = -0.559016994 + 1.25
w = -0.559016994 + 1.25

Combine like terms: -0.559016994 + 1.25 = 0.690983006
w = 0.690983006

Simplifying
w = 0.690983006

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {1.809016994, 0.690983006}
Solution
w = {1.809016994, 0.690983006}