12x(2x-8)=4(5-2x)+3(7-3x)

Solution for 12x(2x-8)=4(5-2x)+3(7-3x) equation:

Simplifying
12x(2x + -8) = 4(5 + -2x) + 3(7 + -3x)

Reorder the terms:
12x(-8 + 2x) = 4(5 + -2x) + 3(7 + -3x)
(-8 * 12x + 2x * 12x) = 4(5 + -2x) + 3(7 + -3x)
(-96x + 24x2) = 4(5 + -2x) + 3(7 + -3x)
-96x + 24x2 = (5 * 4 + -2x * 4) + 3(7 + -3x)
-96x + 24x2 = (20 + -8x) + 3(7 + -3x)
-96x + 24x2 = 20 + -8x + (7 * 3 + -3x * 3)
-96x + 24x2 = 20 + -8x + (21 + -9x)

Reorder the terms:
-96x + 24x2 = 20 + 21 + -8x + -9x

Combine like terms: 20 + 21 = 41
-96x + 24x2 = 41 + -8x + -9x

Combine like terms: -8x + -9x = -17x
-96x + 24x2 = 41 + -17x

Solving
-96x + 24x2 = 41 + -17x

Solving for variable 'x'.

Reorder the terms:
-41 + -96x + 17x + 24x2 = 41 + -17x + -41 + 17x

Combine like terms: -96x + 17x = -79x
-41 + -79x + 24x2 = 41 + -17x + -41 + 17x

Reorder the terms:
-41 + -79x + 24x2 = 41 + -41 + -17x + 17x

Combine like terms: 41 + -41 = 0
-41 + -79x + 24x2 = 0 + -17x + 17x
-41 + -79x + 24x2 = -17x + 17x

Combine like terms: -17x + 17x = 0
-41 + -79x + 24x2 = 0

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

Divide each side by '24'.
-1.708333333 + -3.291666667x + x2 = 0

Move the constant term to the right:

Add '1.708333333' to each side of the equation.
-1.708333333 + -3.291666667x + 1.708333333 + x2 = 0 + 1.708333333

Reorder the terms:
-1.708333333 + 1.708333333 + -3.291666667x + x2 = 0 + 1.708333333

Combine like terms: -1.708333333 + 1.708333333 = 0.000000000
0.000000000 + -3.291666667x + x2 = 0 + 1.708333333
-3.291666667x + x2 = 0 + 1.708333333

Combine like terms: 0 + 1.708333333 = 1.708333333
-3.291666667x + x2 = 1.708333333

The x term is -3.291666667x.  Take half its coefficient (-1.645833334).
Square it (2.708767363) and add it to both sides.

Add '2.708767363' to each side of the equation.
-3.291666667x + 2.708767363 + x2 = 1.708333333 + 2.708767363

Reorder the terms:
2.708767363 + -3.291666667x + x2 = 1.708333333 + 2.708767363

Combine like terms: 1.708333333 + 2.708767363 = 4.417100696
2.708767363 + -3.291666667x + x2 = 4.417100696

Factor a perfect square on the left side:
(x + -1.645833334)(x + -1.645833334) = 4.417100696

Calculate the square root of the right side: 2.101689962

Break this problem into two subproblems by setting 
(x + -1.645833334) equal to 2.101689962 and -2.101689962.

Subproblem 1
x + -1.645833334 = 2.101689962

Simplifying
x + -1.645833334 = 2.101689962

Reorder the terms:
-1.645833334 + x = 2.101689962

Solving
-1.645833334 + x = 2.101689962

Solving for variable 'x'.

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

Add '1.645833334' to each side of the equation.
-1.645833334 + 1.645833334 + x = 2.101689962 + 1.645833334

Combine like terms: -1.645833334 + 1.645833334 = 0.000000000
0.000000000 + x = 2.101689962 + 1.645833334
x = 2.101689962 + 1.645833334

Combine like terms: 2.101689962 + 1.645833334 = 3.747523296
x = 3.747523296

Simplifying
x = 3.747523296

Subproblem 2
x + -1.645833334 = -2.101689962

Simplifying
x + -1.645833334 = -2.101689962

Reorder the terms:
-1.645833334 + x = -2.101689962

Solving
-1.645833334 + x = -2.101689962

Solving for variable 'x'.

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

Add '1.645833334' to each side of the equation.
-1.645833334 + 1.645833334 + x = -2.101689962 + 1.645833334

Combine like terms: -1.645833334 + 1.645833334 = 0.000000000
0.000000000 + x = -2.101689962 + 1.645833334
x = -2.101689962 + 1.645833334

Combine like terms: -2.101689962 + 1.645833334 = -0.455856628
x = -0.455856628

Simplifying
x = -0.455856628

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.747523296, -0.455856628}