(w+5-2)(w-2)(2)=266

Solution for (w+5-2)(w-2)(2)=266 equation:

Simplifying
(w + 5 + -2)(w + -2)(2) = 266

Reorder the terms:
(5 + -2 + w)(w + -2)(2) = 266

Combine like terms: 5 + -2 = 3
(3 + w)(w + -2)(2) = 266

Reorder the terms:
(3 + w)(-2 + w)(2) = 266

Reorder the terms for easier multiplication:
2(3 + w)(-2 + w) = 266

Multiply (3 + w) * (-2 + w)
2(3(-2 + w) + w(-2 + w)) = 266
2((-2 * 3 + w * 3) + w(-2 + w)) = 266
2((-6 + 3w) + w(-2 + w)) = 266
2(-6 + 3w + (-2 * w + w * w)) = 266
2(-6 + 3w + (-2w + w2)) = 266

Combine like terms: 3w + -2w = 1w
2(-6 + 1w + w2) = 266
(-6 * 2 + 1w * 2 + w2 * 2) = 266
(-12 + 2w + 2w2) = 266

Solving
-12 + 2w + 2w2 = 266

Solving for variable 'w'.

Reorder the terms:
-12 + -266 + 2w + 2w2 = 266 + -266

Combine like terms: -12 + -266 = -278
-278 + 2w + 2w2 = 266 + -266

Combine like terms: 266 + -266 = 0
-278 + 2w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-139 + w + w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-139 + w + w2)' equal to zero and attempt to solve:

Simplifying
-139 + w + w2 = 0

Solving
-139 + w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '139' to each side of the equation.
-139 + w + 139 + w2 = 0 + 139

Reorder the terms:
-139 + 139 + w + w2 = 0 + 139

Combine like terms: -139 + 139 = 0
0 + w + w2 = 0 + 139
w + w2 = 0 + 139

Combine like terms: 0 + 139 = 139
w + w2 = 139

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.
w + 0.25 + w2 = 139 + 0.25

Reorder the terms:
0.25 + w + w2 = 139 + 0.25

Combine like terms: 139 + 0.25 = 139.25
0.25 + w + w2 = 139.25

Factor a perfect square on the left side:
(w + 0.5)(w + 0.5) = 139.25

Calculate the square root of the right side: 11.800423721

Break this problem into two subproblems by setting 
(w + 0.5) equal to 11.800423721 and -11.800423721.

Subproblem 1
w + 0.5 = 11.800423721

Simplifying
w + 0.5 = 11.800423721

Reorder the terms:
0.5 + w = 11.800423721

Solving
0.5 + w = 11.800423721

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 = 11.800423721 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = 11.800423721 + -0.5
w = 11.800423721 + -0.5

Combine like terms: 11.800423721 + -0.5 = 11.300423721
w = 11.300423721

Simplifying
w = 11.300423721

Subproblem 2
w + 0.5 = -11.800423721

Simplifying
w + 0.5 = -11.800423721

Reorder the terms:
0.5 + w = -11.800423721

Solving
0.5 + w = -11.800423721

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 = -11.800423721 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + w = -11.800423721 + -0.5
w = -11.800423721 + -0.5

Combine like terms: -11.800423721 + -0.5 = -12.300423721
w = -12.300423721

Simplifying
w = -12.300423721

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {11.300423721, -12.300423721}
Solution
w = {11.300423721, -12.300423721}