6(x-4)2(x+12)-2x=3(x-2)

Solution for 6(x-4)2(x+12)-2x=3(x-2) equation:

Simplifying
6(x + -4) * 2(x + 12) + -2x = 3(x + -2)

Reorder the terms:
6(-4 + x) * 2(x + 12) + -2x = 3(x + -2)

Reorder the terms:
6(-4 + x) * 2(12 + x) + -2x = 3(x + -2)

Reorder the terms for easier multiplication:
6 * 2(-4 + x)(12 + x) + -2x = 3(x + -2)

Multiply 6 * 2
12(-4 + x)(12 + x) + -2x = 3(x + -2)

Multiply (-4 + x) * (12 + x)
12(-4(12 + x) + x(12 + x)) + -2x = 3(x + -2)
12((12 * -4 + x * -4) + x(12 + x)) + -2x = 3(x + -2)
12((-48 + -4x) + x(12 + x)) + -2x = 3(x + -2)
12(-48 + -4x + (12 * x + x * x)) + -2x = 3(x + -2)
12(-48 + -4x + (12x + x2)) + -2x = 3(x + -2)

Combine like terms: -4x + 12x = 8x
12(-48 + 8x + x2) + -2x = 3(x + -2)
(-48 * 12 + 8x * 12 + x2 * 12) + -2x = 3(x + -2)
(-576 + 96x + 12x2) + -2x = 3(x + -2)

Reorder the terms:
-576 + 96x + -2x + 12x2 = 3(x + -2)

Combine like terms: 96x + -2x = 94x
-576 + 94x + 12x2 = 3(x + -2)

Reorder the terms:
-576 + 94x + 12x2 = 3(-2 + x)
-576 + 94x + 12x2 = (-2 * 3 + x * 3)
-576 + 94x + 12x2 = (-6 + 3x)

Solving
-576 + 94x + 12x2 = -6 + 3x

Solving for variable 'x'.

Reorder the terms:
-576 + 6 + 94x + -3x + 12x2 = -6 + 3x + 6 + -3x

Combine like terms: -576 + 6 = -570
-570 + 94x + -3x + 12x2 = -6 + 3x + 6 + -3x

Combine like terms: 94x + -3x = 91x
-570 + 91x + 12x2 = -6 + 3x + 6 + -3x

Reorder the terms:
-570 + 91x + 12x2 = -6 + 6 + 3x + -3x

Combine like terms: -6 + 6 = 0
-570 + 91x + 12x2 = 0 + 3x + -3x
-570 + 91x + 12x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-570 + 91x + 12x2 = 0

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

Divide each side by '12'.
-47.5 + 7.583333333x + x2 = 0

Move the constant term to the right:

Add '47.5' to each side of the equation.
-47.5 + 7.583333333x + 47.5 + x2 = 0 + 47.5

Reorder the terms:
-47.5 + 47.5 + 7.583333333x + x2 = 0 + 47.5

Combine like terms: -47.5 + 47.5 = 0.0
0.0 + 7.583333333x + x2 = 0 + 47.5
7.583333333x + x2 = 0 + 47.5

Combine like terms: 0 + 47.5 = 47.5
7.583333333x + x2 = 47.5

The x term is 7.583333333x.  Take half its coefficient (3.791666667).
Square it (14.37673611) and add it to both sides.

Add '14.37673611' to each side of the equation.
7.583333333x + 14.37673611 + x2 = 47.5 + 14.37673611

Reorder the terms:
14.37673611 + 7.583333333x + x2 = 47.5 + 14.37673611

Combine like terms: 47.5 + 14.37673611 = 61.87673611
14.37673611 + 7.583333333x + x2 = 61.87673611

Factor a perfect square on the left side:
(x + 3.791666667)(x + 3.791666667) = 61.87673611

Calculate the square root of the right side: 7.866176715

Break this problem into two subproblems by setting 
(x + 3.791666667) equal to 7.866176715 and -7.866176715.

Subproblem 1
x + 3.791666667 = 7.866176715

Simplifying
x + 3.791666667 = 7.866176715

Reorder the terms:
3.791666667 + x = 7.866176715

Solving
3.791666667 + x = 7.866176715

Solving for variable 'x'.

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

Add '-3.791666667' to each side of the equation.
3.791666667 + -3.791666667 + x = 7.866176715 + -3.791666667

Combine like terms: 3.791666667 + -3.791666667 = 0.000000000
0.000000000 + x = 7.866176715 + -3.791666667
x = 7.866176715 + -3.791666667

Combine like terms: 7.866176715 + -3.791666667 = 4.074510048
x = 4.074510048

Simplifying
x = 4.074510048

Subproblem 2
x + 3.791666667 = -7.866176715

Simplifying
x + 3.791666667 = -7.866176715

Reorder the terms:
3.791666667 + x = -7.866176715

Solving
3.791666667 + x = -7.866176715

Solving for variable 'x'.

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

Add '-3.791666667' to each side of the equation.
3.791666667 + -3.791666667 + x = -7.866176715 + -3.791666667

Combine like terms: 3.791666667 + -3.791666667 = 0.000000000
0.000000000 + x = -7.866176715 + -3.791666667
x = -7.866176715 + -3.791666667

Combine like terms: -7.866176715 + -3.791666667 = -11.657843382
x = -11.657843382

Simplifying
x = -11.657843382

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.074510048, -11.657843382}