380=2(w)(w+20)

Solution for 380=2(w)(w+20) equation:

Simplifying
380 = 2(w)(w + 20)

Reorder the terms:
380 = 2w(20 + w)
380 = (20 * 2w + w * 2w)
380 = (40w + 2w2)

Solving
380 = 40w + 2w2

Solving for variable 'w'.

Reorder the terms:
380 + -40w + -2w2 = 40w + -40w + 2w2 + -2w2

Combine like terms: 40w + -40w = 0
380 + -40w + -2w2 = 0 + 2w2 + -2w2
380 + -40w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
380 + -40w + -2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(190 + -20w + -1w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(190 + -20w + -1w2)' equal to zero and attempt to solve:

Simplifying
190 + -20w + -1w2 = 0

Solving
190 + -20w + -1w2 = 0

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

Divide each side by '-1'.
-190 + 20w + w2 = 0

Move the constant term to the right:

Add '190' to each side of the equation.
-190 + 20w + 190 + w2 = 0 + 190

Reorder the terms:
-190 + 190 + 20w + w2 = 0 + 190

Combine like terms: -190 + 190 = 0
0 + 20w + w2 = 0 + 190
20w + w2 = 0 + 190

Combine like terms: 0 + 190 = 190
20w + w2 = 190

The w term is 20w.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20w + 100 + w2 = 190 + 100

Reorder the terms:
100 + 20w + w2 = 190 + 100

Combine like terms: 190 + 100 = 290
100 + 20w + w2 = 290

Factor a perfect square on the left side:
(w + 10)(w + 10) = 290

Calculate the square root of the right side: 17.029386366

Break this problem into two subproblems by setting 
(w + 10) equal to 17.029386366 and -17.029386366.

Subproblem 1
w + 10 = 17.029386366

Simplifying
w + 10 = 17.029386366

Reorder the terms:
10 + w = 17.029386366

Solving
10 + w = 17.029386366

Solving for variable 'w'.

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

Add '-10' to each side of the equation.
10 + -10 + w = 17.029386366 + -10

Combine like terms: 10 + -10 = 0
0 + w = 17.029386366 + -10
w = 17.029386366 + -10

Combine like terms: 17.029386366 + -10 = 7.029386366
w = 7.029386366

Simplifying
w = 7.029386366

Subproblem 2
w + 10 = -17.029386366

Simplifying
w + 10 = -17.029386366

Reorder the terms:
10 + w = -17.029386366

Solving
10 + w = -17.029386366

Solving for variable 'w'.

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

Add '-10' to each side of the equation.
10 + -10 + w = -17.029386366 + -10

Combine like terms: 10 + -10 = 0
0 + w = -17.029386366 + -10
w = -17.029386366 + -10

Combine like terms: -17.029386366 + -10 = -27.029386366
w = -27.029386366

Simplifying
w = -27.029386366

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {7.029386366, -27.029386366}
Solution
w = {7.029386366, -27.029386366}