3(x-2)8x=44

Solution for 3(x-2)8x=44 equation:

Simplifying
3(x + -2) * 8x = 44

Reorder the terms:
3(-2 + x) * 8x = 44

Reorder the terms for easier multiplication:
3 * 8x(-2 + x) = 44

Multiply 3 * 8
24x(-2 + x) = 44
(-2 * 24x + x * 24x) = 44
(-48x + 24x2) = 44

Solving
-48x + 24x2 = 44

Solving for variable 'x'.

Reorder the terms:
-44 + -48x + 24x2 = 44 + -44

Combine like terms: 44 + -44 = 0
-44 + -48x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-11 + -12x + 6x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-11 + -12x + 6x2)' equal to zero and attempt to solve:

Simplifying
-11 + -12x + 6x2 = 0

Solving
-11 + -12x + 6x2 = 0

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

Divide each side by '6'.
-1.833333333 + -2x + x2 = 0

Move the constant term to the right:

Add '1.833333333' to each side of the equation.
-1.833333333 + -2x + 1.833333333 + x2 = 0 + 1.833333333

Reorder the terms:
-1.833333333 + 1.833333333 + -2x + x2 = 0 + 1.833333333

Combine like terms: -1.833333333 + 1.833333333 = 0.000000000
0.000000000 + -2x + x2 = 0 + 1.833333333
-2x + x2 = 0 + 1.833333333

Combine like terms: 0 + 1.833333333 = 1.833333333
-2x + x2 = 1.833333333

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 1.833333333 + 1

Reorder the terms:
1 + -2x + x2 = 1.833333333 + 1

Combine like terms: 1.833333333 + 1 = 2.833333333
1 + -2x + x2 = 2.833333333

Factor a perfect square on the left side:
(x + -1)(x + -1) = 2.833333333

Calculate the square root of the right side: 1.683250823

Break this problem into two subproblems by setting 
(x + -1) equal to 1.683250823 and -1.683250823.

Subproblem 1
x + -1 = 1.683250823

Simplifying
x + -1 = 1.683250823

Reorder the terms:
-1 + x = 1.683250823

Solving
-1 + x = 1.683250823

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 1.683250823 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.683250823 + 1
x = 1.683250823 + 1

Combine like terms: 1.683250823 + 1 = 2.683250823
x = 2.683250823

Simplifying
x = 2.683250823

Subproblem 2
x + -1 = -1.683250823

Simplifying
x + -1 = -1.683250823

Reorder the terms:
-1 + x = -1.683250823

Solving
-1 + x = -1.683250823

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -1.683250823 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.683250823 + 1
x = -1.683250823 + 1

Combine like terms: -1.683250823 + 1 = -0.683250823
x = -0.683250823

Simplifying
x = -0.683250823

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.683250823, -0.683250823}
Solution
x = {2.683250823, -0.683250823}