(2x-6x)(4x+2)=(8x+3)(x-4)

Solution for (2x-6x)(4x+2)=(8x+3)(x-4) equation:

Simplifying
(2x + -6x)(4x + 2) = (8x + 3)(x + -4)

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

Remove parenthesis around (-4x)
-4x(4x + 2) = (8x + 3)(x + -4)

Reorder the terms:
-4x(2 + 4x) = (8x + 3)(x + -4)
(2 * -4x + 4x * -4x) = (8x + 3)(x + -4)
(-8x + -16x2) = (8x + 3)(x + -4)

Reorder the terms:
-8x + -16x2 = (3 + 8x)(x + -4)

Reorder the terms:
-8x + -16x2 = (3 + 8x)(-4 + x)

Multiply (3 + 8x) * (-4 + x)
-8x + -16x2 = (3(-4 + x) + 8x * (-4 + x))
-8x + -16x2 = ((-4 * 3 + x * 3) + 8x * (-4 + x))
-8x + -16x2 = ((-12 + 3x) + 8x * (-4 + x))
-8x + -16x2 = (-12 + 3x + (-4 * 8x + x * 8x))
-8x + -16x2 = (-12 + 3x + (-32x + 8x2))

Combine like terms: 3x + -32x = -29x
-8x + -16x2 = (-12 + -29x + 8x2)

Solving
-8x + -16x2 = -12 + -29x + 8x2

Solving for variable 'x'.

Reorder the terms:
12 + -8x + 29x + -16x2 + -8x2 = -12 + -29x + 8x2 + 12 + 29x + -8x2

Combine like terms: -8x + 29x = 21x
12 + 21x + -16x2 + -8x2 = -12 + -29x + 8x2 + 12 + 29x + -8x2

Combine like terms: -16x2 + -8x2 = -24x2
12 + 21x + -24x2 = -12 + -29x + 8x2 + 12 + 29x + -8x2

Reorder the terms:
12 + 21x + -24x2 = -12 + 12 + -29x + 29x + 8x2 + -8x2

Combine like terms: -12 + 12 = 0
12 + 21x + -24x2 = 0 + -29x + 29x + 8x2 + -8x2
12 + 21x + -24x2 = -29x + 29x + 8x2 + -8x2

Combine like terms: -29x + 29x = 0
12 + 21x + -24x2 = 0 + 8x2 + -8x2
12 + 21x + -24x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
12 + 21x + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + 7x + -8x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(4 + 7x + -8x2)' equal to zero and attempt to solve:

Simplifying
4 + 7x + -8x2 = 0

Solving
4 + 7x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-0.5 + -0.875x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -0.875x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -0.875x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.875x + x2 = 0 + 0.5
-0.875x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-0.875x + x2 = 0.5

The x term is -0.875x.  Take half its coefficient (-0.4375).
Square it (0.19140625) and add it to both sides.

Add '0.19140625' to each side of the equation.
-0.875x + 0.19140625 + x2 = 0.5 + 0.19140625

Reorder the terms:
0.19140625 + -0.875x + x2 = 0.5 + 0.19140625

Combine like terms: 0.5 + 0.19140625 = 0.69140625
0.19140625 + -0.875x + x2 = 0.69140625

Factor a perfect square on the left side:
(x + -0.4375)(x + -0.4375) = 0.69140625

Calculate the square root of the right side: 0.831508418

Break this problem into two subproblems by setting 
(x + -0.4375) equal to 0.831508418 and -0.831508418.

Subproblem 1
x + -0.4375 = 0.831508418

Simplifying
x + -0.4375 = 0.831508418

Reorder the terms:
-0.4375 + x = 0.831508418

Solving
-0.4375 + x = 0.831508418

Solving for variable 'x'.

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

Add '0.4375' to each side of the equation.
-0.4375 + 0.4375 + x = 0.831508418 + 0.4375

Combine like terms: -0.4375 + 0.4375 = 0.0000
0.0000 + x = 0.831508418 + 0.4375
x = 0.831508418 + 0.4375

Combine like terms: 0.831508418 + 0.4375 = 1.269008418
x = 1.269008418

Simplifying
x = 1.269008418

Subproblem 2
x + -0.4375 = -0.831508418

Simplifying
x + -0.4375 = -0.831508418

Reorder the terms:
-0.4375 + x = -0.831508418

Solving
-0.4375 + x = -0.831508418

Solving for variable 'x'.

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

Add '0.4375' to each side of the equation.
-0.4375 + 0.4375 + x = -0.831508418 + 0.4375

Combine like terms: -0.4375 + 0.4375 = 0.0000
0.0000 + x = -0.831508418 + 0.4375
x = -0.831508418 + 0.4375

Combine like terms: -0.831508418 + 0.4375 = -0.394008418
x = -0.394008418

Simplifying
x = -0.394008418

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.269008418, -0.394008418}
Solution
x = {1.269008418, -0.394008418}