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

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

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

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

Combine like terms: x + 3x = 4x
384 = 2(-5 + 4x) + 2(x + 3 + x + -5) * x
384 = (-5 * 2 + 4x * 2) + 2(x + 3 + x + -5) * x
384 = (-10 + 8x) + 2(x + 3 + x + -5) * x

Reorder the terms:
384 = -10 + 8x + 2(3 + -5 + x + x) * x

Combine like terms: 3 + -5 = -2
384 = -10 + 8x + 2(-2 + x + x) * x

Combine like terms: x + x = 2x
384 = -10 + 8x + 2(-2 + 2x) * x

Reorder the terms for easier multiplication:
384 = -10 + 8x + 2x(-2 + 2x)
384 = -10 + 8x + (-2 * 2x + 2x * 2x)
384 = -10 + 8x + (-4x + 4x2)

Combine like terms: 8x + -4x = 4x
384 = -10 + 4x + 4x2

Solving
384 = -10 + 4x + 4x2

Solving for variable 'x'.

Combine like terms: 384 + 10 = 394
394 + -4x + -4x2 = -10 + 4x + 4x2 + 10 + -4x + -4x2

Reorder the terms:
394 + -4x + -4x2 = -10 + 10 + 4x + -4x + 4x2 + -4x2

Combine like terms: -10 + 10 = 0
394 + -4x + -4x2 = 0 + 4x + -4x + 4x2 + -4x2
394 + -4x + -4x2 = 4x + -4x + 4x2 + -4x2

Combine like terms: 4x + -4x = 0
394 + -4x + -4x2 = 0 + 4x2 + -4x2
394 + -4x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
394 + -4x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(197 + -2x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(197 + -2x + -2x2)' equal to zero and attempt to solve:

Simplifying
197 + -2x + -2x2 = 0

Solving
197 + -2x + -2x2 = 0

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

Divide each side by '-2'.
-98.5 + x + x2 = 0

Move the constant term to the right:

Add '98.5' to each side of the equation.
-98.5 + x + 98.5 + x2 = 0 + 98.5

Reorder the terms:
-98.5 + 98.5 + x + x2 = 0 + 98.5

Combine like terms: -98.5 + 98.5 = 0.0
0.0 + x + x2 = 0 + 98.5
x + x2 = 0 + 98.5

Combine like terms: 0 + 98.5 = 98.5
x + x2 = 98.5

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 = 98.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 98.5 + 0.25

Combine like terms: 98.5 + 0.25 = 98.75
1.25 + x2 = 98.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 98.75

Calculate the square root of the right side: 9.937303457

Break this problem into two subproblems by setting 
(x + 0.5) equal to 9.937303457 and -9.937303457.

Subproblem 1
x + 0.5 = 9.937303457

Simplifying
x + 0.5 = 9.937303457

Reorder the terms:
0.5 + x = 9.937303457

Solving
0.5 + x = 9.937303457

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 = 9.937303457 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 9.937303457 + -0.5
x = 9.937303457 + -0.5

Combine like terms: 9.937303457 + -0.5 = 9.437303457
x = 9.437303457

Simplifying
x = 9.437303457

Subproblem 2
x + 0.5 = -9.937303457

Simplifying
x + 0.5 = -9.937303457

Reorder the terms:
0.5 + x = -9.937303457

Solving
0.5 + x = -9.937303457

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 = -9.937303457 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -9.937303457 + -0.5
x = -9.937303457 + -0.5

Combine like terms: -9.937303457 + -0.5 = -10.437303457
x = -10.437303457

Simplifying
x = -10.437303457

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.437303457, -10.437303457}
Solution
x = {9.437303457, -10.437303457}