2(x+3)(x-5)+2(x+3)(x)+2(x)=384

Solution for 2(x+3)(x-5)+2(x+3)(x)+2(x)=384 equation:

Simplifying
2(x + 3)(x + -5) + 2(x + 3)(x) + 2(x) = 384

Reorder the terms:
2(3 + x)(x + -5) + 2(x + 3)(x) + 2(x) = 384

Reorder the terms:
2(3 + x)(-5 + x) + 2(x + 3)(x) + 2(x) = 384

Multiply (3 + x) * (-5 + x)
2(3(-5 + x) + x(-5 + x)) + 2(x + 3)(x) + 2(x) = 384
2((-5 * 3 + x * 3) + x(-5 + x)) + 2(x + 3)(x) + 2(x) = 384
2((-15 + 3x) + x(-5 + x)) + 2(x + 3)(x) + 2(x) = 384
2(-15 + 3x + (-5 * x + x * x)) + 2(x + 3)(x) + 2(x) = 384
2(-15 + 3x + (-5x + x2)) + 2(x + 3)(x) + 2(x) = 384

Combine like terms: 3x + -5x = -2x
2(-15 + -2x + x2) + 2(x + 3)(x) + 2(x) = 384
(-15 * 2 + -2x * 2 + x2 * 2) + 2(x + 3)(x) + 2(x) = 384
(-30 + -4x + 2x2) + 2(x + 3)(x) + 2(x) = 384

Reorder the terms:
-30 + -4x + 2x2 + 2(3 + x)(x) + 2(x) = 384

Reorder the terms for easier multiplication:
-30 + -4x + 2x2 + 2x(3 + x) + 2(x) = 384
-30 + -4x + 2x2 + (3 * 2x + x * 2x) + 2(x) = 384
-30 + -4x + 2x2 + (6x + 2x2) + 2(x) = 384

Reorder the terms:
-30 + -4x + 6x + 2x + 2x2 + 2x2 = 384

Combine like terms: -4x + 6x = 2x
-30 + 2x + 2x + 2x2 + 2x2 = 384

Combine like terms: 2x + 2x = 4x
-30 + 4x + 2x2 + 2x2 = 384

Combine like terms: 2x2 + 2x2 = 4x2
-30 + 4x + 4x2 = 384

Solving
-30 + 4x + 4x2 = 384

Solving for variable 'x'.

Reorder the terms:
-30 + -384 + 4x + 4x2 = 384 + -384

Combine like terms: -30 + -384 = -414
-414 + 4x + 4x2 = 384 + -384

Combine like terms: 384 + -384 = 0
-414 + 4x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-207 + 2x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-207 + 2x + 2x2)' equal to zero and attempt to solve:

Simplifying
-207 + 2x + 2x2 = 0

Solving
-207 + 2x + 2x2 = 0

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

Divide each side by '2'.
-103.5 + x + x2 = 0

Move the constant term to the right:

Add '103.5' to each side of the equation.
-103.5 + x + 103.5 + x2 = 0 + 103.5

Reorder the terms:
-103.5 + 103.5 + x + x2 = 0 + 103.5

Combine like terms: -103.5 + 103.5 = 0.0
0.0 + x + x2 = 0 + 103.5
x + x2 = 0 + 103.5

Combine like terms: 0 + 103.5 = 103.5
x + x2 = 103.5

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.
 + 0.25 + x2 = 103.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 103.5 + 0.25

Combine like terms: 103.5 + 0.25 = 103.75
1.25 + x2 = 103.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 103.75

Calculate the square root of the right side: 10.185774394

Break this problem into two subproblems by setting 
(x + 0.5) equal to 10.185774394 and -10.185774394.

Subproblem 1
x + 0.5 = 10.185774394

Simplifying
x + 0.5 = 10.185774394

Reorder the terms:
0.5 + x = 10.185774394

Solving
0.5 + x = 10.185774394

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 = 10.185774394 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 10.185774394 + -0.5
x = 10.185774394 + -0.5

Combine like terms: 10.185774394 + -0.5 = 9.685774394
x = 9.685774394

Simplifying
x = 9.685774394

Subproblem 2
x + 0.5 = -10.185774394

Simplifying
x + 0.5 = -10.185774394

Reorder the terms:
0.5 + x = -10.185774394

Solving
0.5 + x = -10.185774394

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 = -10.185774394 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -10.185774394 + -0.5
x = -10.185774394 + -0.5

Combine like terms: -10.185774394 + -0.5 = -10.685774394
x = -10.685774394

Simplifying
x = -10.685774394

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.685774394, -10.685774394}
Solution
x = {9.685774394, -10.685774394}