(3x+4)*(x-8)=(7-3x)*(x-4)

Solution for (3x+4)*(x-8)=(7-3x)*(x-4) equation:

Simplifying
(3x + 4)(x + -8) = (7 + -3x)(x + -4)

Reorder the terms:
(4 + 3x)(x + -8) = (7 + -3x)(x + -4)

Reorder the terms:
(4 + 3x)(-8 + x) = (7 + -3x)(x + -4)

Multiply (4 + 3x) * (-8 + x)
(4(-8 + x) + 3x * (-8 + x)) = (7 + -3x)(x + -4)
((-8 * 4 + x * 4) + 3x * (-8 + x)) = (7 + -3x)(x + -4)
((-32 + 4x) + 3x * (-8 + x)) = (7 + -3x)(x + -4)
(-32 + 4x + (-8 * 3x + x * 3x)) = (7 + -3x)(x + -4)
(-32 + 4x + (-24x + 3x2)) = (7 + -3x)(x + -4)

Combine like terms: 4x + -24x = -20x
(-32 + -20x + 3x2) = (7 + -3x)(x + -4)

Reorder the terms:
-32 + -20x + 3x2 = (7 + -3x)(-4 + x)

Multiply (7 + -3x) * (-4 + x)
-32 + -20x + 3x2 = (7(-4 + x) + -3x * (-4 + x))
-32 + -20x + 3x2 = ((-4 * 7 + x * 7) + -3x * (-4 + x))
-32 + -20x + 3x2 = ((-28 + 7x) + -3x * (-4 + x))
-32 + -20x + 3x2 = (-28 + 7x + (-4 * -3x + x * -3x))
-32 + -20x + 3x2 = (-28 + 7x + (12x + -3x2))

Combine like terms: 7x + 12x = 19x
-32 + -20x + 3x2 = (-28 + 19x + -3x2)

Solving
-32 + -20x + 3x2 = -28 + 19x + -3x2

Solving for variable 'x'.

Reorder the terms:
-32 + 28 + -20x + -19x + 3x2 + 3x2 = -28 + 19x + -3x2 + 28 + -19x + 3x2

Combine like terms: -32 + 28 = -4
-4 + -20x + -19x + 3x2 + 3x2 = -28 + 19x + -3x2 + 28 + -19x + 3x2

Combine like terms: -20x + -19x = -39x
-4 + -39x + 3x2 + 3x2 = -28 + 19x + -3x2 + 28 + -19x + 3x2

Combine like terms: 3x2 + 3x2 = 6x2
-4 + -39x + 6x2 = -28 + 19x + -3x2 + 28 + -19x + 3x2

Reorder the terms:
-4 + -39x + 6x2 = -28 + 28 + 19x + -19x + -3x2 + 3x2

Combine like terms: -28 + 28 = 0
-4 + -39x + 6x2 = 0 + 19x + -19x + -3x2 + 3x2
-4 + -39x + 6x2 = 19x + -19x + -3x2 + 3x2

Combine like terms: 19x + -19x = 0
-4 + -39x + 6x2 = 0 + -3x2 + 3x2
-4 + -39x + 6x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-4 + -39x + 6x2 = 0

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

Divide each side by '6'.
-0.6666666667 + -6.5x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -6.5x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -6.5x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -6.5x + x2 = 0 + 0.6666666667
-6.5x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-6.5x + x2 = 0.6666666667

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = 0.6666666667 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = 0.6666666667 + 10.5625

Combine like terms: 0.6666666667 + 10.5625 = 11.2291666667
10.5625 + -6.5x + x2 = 11.2291666667

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 11.2291666667

Calculate the square root of the right side: 3.350994877

Break this problem into two subproblems by setting 
(x + -3.25) equal to 3.350994877 and -3.350994877.

Subproblem 1
x + -3.25 = 3.350994877

Simplifying
x + -3.25 = 3.350994877

Reorder the terms:
-3.25 + x = 3.350994877

Solving
-3.25 + x = 3.350994877

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = 3.350994877 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = 3.350994877 + 3.25
x = 3.350994877 + 3.25

Combine like terms: 3.350994877 + 3.25 = 6.600994877
x = 6.600994877

Simplifying
x = 6.600994877

Subproblem 2
x + -3.25 = -3.350994877

Simplifying
x + -3.25 = -3.350994877

Reorder the terms:
-3.25 + x = -3.350994877

Solving
-3.25 + x = -3.350994877

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = -3.350994877 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = -3.350994877 + 3.25
x = -3.350994877 + 3.25

Combine like terms: -3.350994877 + 3.25 = -0.100994877
x = -0.100994877

Simplifying
x = -0.100994877

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.600994877, -0.100994877}