2w+20=(w+5)(w-5)

Solution for 2w+20=(w+5)(w-5) equation:

Simplifying
2w + 20 = (w + 5)(w + -5)

Reorder the terms:
20 + 2w = (w + 5)(w + -5)

Reorder the terms:
20 + 2w = (5 + w)(w + -5)

Reorder the terms:
20 + 2w = (5 + w)(-5 + w)

Multiply (5 + w) * (-5 + w)
20 + 2w = (5(-5 + w) + w(-5 + w))
20 + 2w = ((-5 * 5 + w * 5) + w(-5 + w))
20 + 2w = ((-25 + 5w) + w(-5 + w))
20 + 2w = (-25 + 5w + (-5 * w + w * w))
20 + 2w = (-25 + 5w + (-5w + w2))

Combine like terms: 5w + -5w = 0
20 + 2w = (-25 + 0 + w2)
20 + 2w = (-25 + w2)

Solving
20 + 2w = -25 + w2

Solving for variable 'w'.

Reorder the terms:
20 + 25 + 2w + -1w2 = -25 + w2 + 25 + -1w2

Combine like terms: 20 + 25 = 45
45 + 2w + -1w2 = -25 + w2 + 25 + -1w2

Reorder the terms:
45 + 2w + -1w2 = -25 + 25 + w2 + -1w2

Combine like terms: -25 + 25 = 0
45 + 2w + -1w2 = 0 + w2 + -1w2
45 + 2w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
45 + 2w + -1w2 = 0

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

Divide each side by '-1'.
-45 + -2w + w2 = 0

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + -2w + 45 + w2 = 0 + 45

Reorder the terms:
-45 + 45 + -2w + w2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + -2w + w2 = 0 + 45
-2w + w2 = 0 + 45

Combine like terms: 0 + 45 = 45
-2w + w2 = 45

The w term is -2w.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2w + 1 + w2 = 45 + 1

Reorder the terms:
1 + -2w + w2 = 45 + 1

Combine like terms: 45 + 1 = 46
1 + -2w + w2 = 46

Factor a perfect square on the left side:
(w + -1)(w + -1) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(w + -1) equal to 6.782329983 and -6.782329983.

Subproblem 1
w + -1 = 6.782329983

Simplifying
w + -1 = 6.782329983

Reorder the terms:
-1 + w = 6.782329983

Solving
-1 + w = 6.782329983

Solving for variable 'w'.

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

Add '1' to each side of the equation.
-1 + 1 + w = 6.782329983 + 1

Combine like terms: -1 + 1 = 0
0 + w = 6.782329983 + 1
w = 6.782329983 + 1

Combine like terms: 6.782329983 + 1 = 7.782329983
w = 7.782329983

Simplifying
w = 7.782329983

Subproblem 2
w + -1 = -6.782329983

Simplifying
w + -1 = -6.782329983

Reorder the terms:
-1 + w = -6.782329983

Solving
-1 + w = -6.782329983

Solving for variable 'w'.

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

Add '1' to each side of the equation.
-1 + 1 + w = -6.782329983 + 1

Combine like terms: -1 + 1 = 0
0 + w = -6.782329983 + 1
w = -6.782329983 + 1

Combine like terms: -6.782329983 + 1 = -5.782329983
w = -5.782329983

Simplifying
w = -5.782329983

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {7.782329983, -5.782329983}