8(x-2)-4(3x+1)-2x=-3x(2x+8)-4(x-4)

Solution for 8(x-2)-4(3x+1)-2x=-3x(2x+8)-4(x-4) equation:

Simplifying
8(x + -2) + -4(3x + 1) + -2x = -3x(2x + 8) + -4(x + -4)

Reorder the terms:
8(-2 + x) + -4(3x + 1) + -2x = -3x(2x + 8) + -4(x + -4)
(-2 * 8 + x * 8) + -4(3x + 1) + -2x = -3x(2x + 8) + -4(x + -4)
(-16 + 8x) + -4(3x + 1) + -2x = -3x(2x + 8) + -4(x + -4)

Reorder the terms:
-16 + 8x + -4(1 + 3x) + -2x = -3x(2x + 8) + -4(x + -4)
-16 + 8x + (1 * -4 + 3x * -4) + -2x = -3x(2x + 8) + -4(x + -4)
-16 + 8x + (-4 + -12x) + -2x = -3x(2x + 8) + -4(x + -4)

Reorder the terms:
-16 + -4 + 8x + -12x + -2x = -3x(2x + 8) + -4(x + -4)

Combine like terms: -16 + -4 = -20
-20 + 8x + -12x + -2x = -3x(2x + 8) + -4(x + -4)

Combine like terms: 8x + -12x = -4x
-20 + -4x + -2x = -3x(2x + 8) + -4(x + -4)

Combine like terms: -4x + -2x = -6x
-20 + -6x = -3x(2x + 8) + -4(x + -4)

Reorder the terms:
-20 + -6x = -3x(8 + 2x) + -4(x + -4)
-20 + -6x = (8 * -3x + 2x * -3x) + -4(x + -4)
-20 + -6x = (-24x + -6x2) + -4(x + -4)

Reorder the terms:
-20 + -6x = -24x + -6x2 + -4(-4 + x)
-20 + -6x = -24x + -6x2 + (-4 * -4 + x * -4)
-20 + -6x = -24x + -6x2 + (16 + -4x)

Reorder the terms:
-20 + -6x = 16 + -24x + -4x + -6x2

Combine like terms: -24x + -4x = -28x
-20 + -6x = 16 + -28x + -6x2

Solving
-20 + -6x = 16 + -28x + -6x2

Solving for variable 'x'.

Reorder the terms:
-20 + -16 + -6x + 28x + 6x2 = 16 + -28x + -6x2 + -16 + 28x + 6x2

Combine like terms: -20 + -16 = -36
-36 + -6x + 28x + 6x2 = 16 + -28x + -6x2 + -16 + 28x + 6x2

Combine like terms: -6x + 28x = 22x
-36 + 22x + 6x2 = 16 + -28x + -6x2 + -16 + 28x + 6x2

Reorder the terms:
-36 + 22x + 6x2 = 16 + -16 + -28x + 28x + -6x2 + 6x2

Combine like terms: 16 + -16 = 0
-36 + 22x + 6x2 = 0 + -28x + 28x + -6x2 + 6x2
-36 + 22x + 6x2 = -28x + 28x + -6x2 + 6x2

Combine like terms: -28x + 28x = 0
-36 + 22x + 6x2 = 0 + -6x2 + 6x2
-36 + 22x + 6x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
-36 + 22x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + 11x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-18 + 11x + 3x2)' equal to zero and attempt to solve:

Simplifying
-18 + 11x + 3x2 = 0

Solving
-18 + 11x + 3x2 = 0

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

Divide each side by '3'.
-6 + 3.666666667x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 3.666666667x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 3.666666667x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 3.666666667x + x2 = 0 + 6
3.666666667x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
3.666666667x + x2 = 6

The x term is 3.666666667x.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667x + 3.361111114 + x2 = 6 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667x + x2 = 6 + 3.361111114

Combine like terms: 6 + 3.361111114 = 9.361111114
3.361111114 + 3.666666667x + x2 = 9.361111114

Factor a perfect square on the left side:
(x + 1.833333334)(x + 1.833333334) = 9.361111114

Calculate the square root of the right side: 3.059593292

Break this problem into two subproblems by setting 
(x + 1.833333334) equal to 3.059593292 and -3.059593292.

Subproblem 1
x + 1.833333334 = 3.059593292

Simplifying
x + 1.833333334 = 3.059593292

Reorder the terms:
1.833333334 + x = 3.059593292

Solving
1.833333334 + x = 3.059593292

Solving for variable 'x'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + x = 3.059593292 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + x = 3.059593292 + -1.833333334
x = 3.059593292 + -1.833333334

Combine like terms: 3.059593292 + -1.833333334 = 1.226259958
x = 1.226259958

Simplifying
x = 1.226259958

Subproblem 2
x + 1.833333334 = -3.059593292

Simplifying
x + 1.833333334 = -3.059593292

Reorder the terms:
1.833333334 + x = -3.059593292

Solving
1.833333334 + x = -3.059593292

Solving for variable 'x'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + x = -3.059593292 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + x = -3.059593292 + -1.833333334
x = -3.059593292 + -1.833333334

Combine like terms: -3.059593292 + -1.833333334 = -4.892926626
x = -4.892926626

Simplifying
x = -4.892926626

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.226259958, -4.892926626}
Solution
x = {1.226259958, -4.892926626}