2(w+5)(w-2)=190

Solution for 2(w+5)(w-2)=190 equation:

Simplifying
2(w + 5)(w + -2) = 190

Reorder the terms:
2(5 + w)(w + -2) = 190

Reorder the terms:
2(5 + w)(-2 + w) = 190

Multiply (5 + w) * (-2 + w)
2(5(-2 + w) + w(-2 + w)) = 190
2((-2 * 5 + w * 5) + w(-2 + w)) = 190
2((-10 + 5w) + w(-2 + w)) = 190
2(-10 + 5w + (-2 * w + w * w)) = 190
2(-10 + 5w + (-2w + w2)) = 190

Combine like terms: 5w + -2w = 3w
2(-10 + 3w + w2) = 190
(-10 * 2 + 3w * 2 + w2 * 2) = 190
(-20 + 6w + 2w2) = 190

Solving
-20 + 6w + 2w2 = 190

Solving for variable 'w'.

Reorder the terms:
-20 + -190 + 6w + 2w2 = 190 + -190

Combine like terms: -20 + -190 = -210
-210 + 6w + 2w2 = 190 + -190

Combine like terms: 190 + -190 = 0
-210 + 6w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-105 + 3w + w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-105 + 3w + w2)' equal to zero and attempt to solve:

Simplifying
-105 + 3w + w2 = 0

Solving
-105 + 3w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '105' to each side of the equation.
-105 + 3w + 105 + w2 = 0 + 105

Reorder the terms:
-105 + 105 + 3w + w2 = 0 + 105

Combine like terms: -105 + 105 = 0
0 + 3w + w2 = 0 + 105
3w + w2 = 0 + 105

Combine like terms: 0 + 105 = 105
3w + w2 = 105

The w term is 3w.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3w + 2.25 + w2 = 105 + 2.25

Reorder the terms:
2.25 + 3w + w2 = 105 + 2.25

Combine like terms: 105 + 2.25 = 107.25
2.25 + 3w + w2 = 107.25

Factor a perfect square on the left side:
(w + 1.5)(w + 1.5) = 107.25

Calculate the square root of the right side: 10.356157589

Break this problem into two subproblems by setting 
(w + 1.5) equal to 10.356157589 and -10.356157589.

Subproblem 1
w + 1.5 = 10.356157589

Simplifying
w + 1.5 = 10.356157589

Reorder the terms:
1.5 + w = 10.356157589

Solving
1.5 + w = 10.356157589

Solving for variable 'w'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + w = 10.356157589 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = 10.356157589 + -1.5
w = 10.356157589 + -1.5

Combine like terms: 10.356157589 + -1.5 = 8.856157589
w = 8.856157589

Simplifying
w = 8.856157589

Subproblem 2
w + 1.5 = -10.356157589

Simplifying
w + 1.5 = -10.356157589

Reorder the terms:
1.5 + w = -10.356157589

Solving
1.5 + w = -10.356157589

Solving for variable 'w'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + w = -10.356157589 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + w = -10.356157589 + -1.5
w = -10.356157589 + -1.5

Combine like terms: -10.356157589 + -1.5 = -11.856157589
w = -11.856157589

Simplifying
w = -11.856157589

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {8.856157589, -11.856157589}
Solution
w = {8.856157589, -11.856157589}