(5-3x)-(-4x+6)=(8x+11)(3x-6)

Solution for (5-3x)-(-4x+6)=(8x+11)(3x-6) equation:

Simplifying
(5 + -3x) + -1(-4x + 6) = (8x + 11)(3x + -6)

Remove parenthesis around (5 + -3x)
5 + -3x + -1(-4x + 6) = (8x + 11)(3x + -6)

Reorder the terms:
5 + -3x + -1(6 + -4x) = (8x + 11)(3x + -6)
5 + -3x + (6 * -1 + -4x * -1) = (8x + 11)(3x + -6)
5 + -3x + (-6 + 4x) = (8x + 11)(3x + -6)

Reorder the terms:
5 + -6 + -3x + 4x = (8x + 11)(3x + -6)

Combine like terms: 5 + -6 = -1
-1 + -3x + 4x = (8x + 11)(3x + -6)

Combine like terms: -3x + 4x = 1x
-1 + 1x = (8x + 11)(3x + -6)

Reorder the terms:
-1 + 1x = (11 + 8x)(3x + -6)

Reorder the terms:
-1 + 1x = (11 + 8x)(-6 + 3x)

Multiply (11 + 8x) * (-6 + 3x)
-1 + 1x = (11(-6 + 3x) + 8x * (-6 + 3x))
-1 + 1x = ((-6 * 11 + 3x * 11) + 8x * (-6 + 3x))
-1 + 1x = ((-66 + 33x) + 8x * (-6 + 3x))
-1 + 1x = (-66 + 33x + (-6 * 8x + 3x * 8x))
-1 + 1x = (-66 + 33x + (-48x + 24x2))

Combine like terms: 33x + -48x = -15x
-1 + 1x = (-66 + -15x + 24x2)

Solving
-1 + 1x = -66 + -15x + 24x2

Solving for variable 'x'.

Reorder the terms:
-1 + 66 + 1x + 15x + -24x2 = -66 + -15x + 24x2 + 66 + 15x + -24x2

Combine like terms: -1 + 66 = 65
65 + 1x + 15x + -24x2 = -66 + -15x + 24x2 + 66 + 15x + -24x2

Combine like terms: 1x + 15x = 16x
65 + 16x + -24x2 = -66 + -15x + 24x2 + 66 + 15x + -24x2

Reorder the terms:
65 + 16x + -24x2 = -66 + 66 + -15x + 15x + 24x2 + -24x2

Combine like terms: -66 + 66 = 0
65 + 16x + -24x2 = 0 + -15x + 15x + 24x2 + -24x2
65 + 16x + -24x2 = -15x + 15x + 24x2 + -24x2

Combine like terms: -15x + 15x = 0
65 + 16x + -24x2 = 0 + 24x2 + -24x2
65 + 16x + -24x2 = 24x2 + -24x2

Combine like terms: 24x2 + -24x2 = 0
65 + 16x + -24x2 = 0

Begin completing the square.  Divide all terms by
-24 the coefficient of the squared term: 

Divide each side by '-24'.
-2.708333333 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '2.708333333' to each side of the equation.
-2.708333333 + -0.6666666667x + 2.708333333 + x2 = 0 + 2.708333333

Reorder the terms:
-2.708333333 + 2.708333333 + -0.6666666667x + x2 = 0 + 2.708333333

Combine like terms: -2.708333333 + 2.708333333 = 0.000000000
0.000000000 + -0.6666666667x + x2 = 0 + 2.708333333
-0.6666666667x + x2 = 0 + 2.708333333

Combine like terms: 0 + 2.708333333 = 2.708333333
-0.6666666667x + x2 = 2.708333333

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = 2.708333333 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 2.708333333 + 0.1111111112

Combine like terms: 2.708333333 + 0.1111111112 = 2.8194444442
0.1111111112 + -0.6666666667x + x2 = 2.8194444442

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 2.8194444442

Calculate the square root of the right side: 1.67912014

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 1.67912014 and -1.67912014.

Subproblem 1
x + -0.3333333334 = 1.67912014

Simplifying
x + -0.3333333334 = 1.67912014

Reorder the terms:
-0.3333333334 + x = 1.67912014

Solving
-0.3333333334 + x = 1.67912014

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = 1.67912014 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = 1.67912014 + 0.3333333334
x = 1.67912014 + 0.3333333334

Combine like terms: 1.67912014 + 0.3333333334 = 2.0124534734
x = 2.0124534734

Simplifying
x = 2.0124534734

Subproblem 2
x + -0.3333333334 = -1.67912014

Simplifying
x + -0.3333333334 = -1.67912014

Reorder the terms:
-0.3333333334 + x = -1.67912014

Solving
-0.3333333334 + x = -1.67912014

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = -1.67912014 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = -1.67912014 + 0.3333333334
x = -1.67912014 + 0.3333333334

Combine like terms: -1.67912014 + 0.3333333334 = -1.3457868066
x = -1.3457868066

Simplifying
x = -1.3457868066

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.0124534734, -1.3457868066}