3(2x-4)2x=68

Solution for 3(2x-4)2x=68 equation:

Simplifying
3(2x + -4) * 2x = 68

Reorder the terms:
3(-4 + 2x) * 2x = 68

Reorder the terms for easier multiplication:
3 * 2x(-4 + 2x) = 68

Multiply 3 * 2
6x(-4 + 2x) = 68
(-4 * 6x + 2x * 6x) = 68
(-24x + 12x2) = 68

Solving
-24x + 12x2 = 68

Solving for variable 'x'.

Reorder the terms:
-68 + -24x + 12x2 = 68 + -68

Combine like terms: 68 + -68 = 0
-68 + -24x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-17 + -6x + 3x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-17 + -6x + 3x2)' equal to zero and attempt to solve:

Simplifying
-17 + -6x + 3x2 = 0

Solving
-17 + -6x + 3x2 = 0

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

Divide each side by '3'.
-5.666666667 + -2x + x2 = 0

Move the constant term to the right:

Add '5.666666667' to each side of the equation.
-5.666666667 + -2x + 5.666666667 + x2 = 0 + 5.666666667

Reorder the terms:
-5.666666667 + 5.666666667 + -2x + x2 = 0 + 5.666666667

Combine like terms: -5.666666667 + 5.666666667 = 0.000000000
0.000000000 + -2x + x2 = 0 + 5.666666667
-2x + x2 = 0 + 5.666666667

Combine like terms: 0 + 5.666666667 = 5.666666667
-2x + x2 = 5.666666667

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 = 5.666666667 + 1

Reorder the terms:
1 + -2x + x2 = 5.666666667 + 1

Combine like terms: 5.666666667 + 1 = 6.666666667
1 + -2x + x2 = 6.666666667

Factor a perfect square on the left side:
(x + -1)(x + -1) = 6.666666667

Calculate the square root of the right side: 2.581988898

Break this problem into two subproblems by setting 
(x + -1) equal to 2.581988898 and -2.581988898.

Subproblem 1
x + -1 = 2.581988898

Simplifying
x + -1 = 2.581988898

Reorder the terms:
-1 + x = 2.581988898

Solving
-1 + x = 2.581988898

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 = 2.581988898 + 1

Combine like terms: -1 + 1 = 0
0 + x = 2.581988898 + 1
x = 2.581988898 + 1

Combine like terms: 2.581988898 + 1 = 3.581988898
x = 3.581988898

Simplifying
x = 3.581988898

Subproblem 2
x + -1 = -2.581988898

Simplifying
x + -1 = -2.581988898

Reorder the terms:
-1 + x = -2.581988898

Solving
-1 + x = -2.581988898

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 = -2.581988898 + 1

Combine like terms: -1 + 1 = 0
0 + x = -2.581988898 + 1
x = -2.581988898 + 1

Combine like terms: -2.581988898 + 1 = -1.581988898
x = -1.581988898

Simplifying
x = -1.581988898

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.581988898, -1.581988898}
Solution
x = {3.581988898, -1.581988898}