(x+3)(x-2)(2)=266

Solution for (x+3)(x-2)(2)=266 equation:

Simplifying
(x + 3)(x + -2)(2) = 266

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

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

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

Multiply (3 + x) * (-2 + x)
2(3(-2 + x) + x(-2 + x)) = 266
2((-2 * 3 + x * 3) + x(-2 + x)) = 266
2((-6 + 3x) + x(-2 + x)) = 266
2(-6 + 3x + (-2 * x + x * x)) = 266
2(-6 + 3x + (-2x + x2)) = 266

Combine like terms: 3x + -2x = 1x
2(-6 + 1x + x2) = 266
(-6 * 2 + 1x * 2 + x2 * 2) = 266
(-12 + 2x + 2x2) = 266

Solving
-12 + 2x + 2x2 = 266

Solving for variable 'x'.

Reorder the terms:
-12 + -266 + 2x + 2x2 = 266 + -266

Combine like terms: -12 + -266 = -278
-278 + 2x + 2x2 = 266 + -266

Combine like terms: 266 + -266 = 0
-278 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-139 + x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-139 + x + x2)' equal to zero and attempt to solve:

Simplifying
-139 + x + x2 = 0

Solving
-139 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '139' to each side of the equation.
-139 + x + 139 + x2 = 0 + 139

Reorder the terms:
-139 + 139 + x + x2 = 0 + 139

Combine like terms: -139 + 139 = 0
0 + x + x2 = 0 + 139
x + x2 = 0 + 139

Combine like terms: 0 + 139 = 139
x + x2 = 139

The x term is x.  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.
x + 0.25 + x2 = 139 + 0.25

Reorder the terms:
0.25 + x + x2 = 139 + 0.25

Combine like terms: 139 + 0.25 = 139.25
0.25 + x + x2 = 139.25

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

Calculate the square root of the right side: 11.800423721

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

Subproblem 1
x + 0.5 = 11.800423721

Simplifying
x + 0.5 = 11.800423721

Reorder the terms:
0.5 + x = 11.800423721

Solving
0.5 + x = 11.800423721

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 11.800423721 + -0.5

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

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

Simplifying
x = 11.300423721

Subproblem 2
x + 0.5 = -11.800423721

Simplifying
x + 0.5 = -11.800423721

Reorder the terms:
0.5 + x = -11.800423721

Solving
0.5 + x = -11.800423721

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -11.800423721 + -0.5

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

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

Simplifying
x = -12.300423721

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