6(x-2)4x=16

Solution for 6(x-2)4x=16 equation:

Simplifying
6(x + -2) * 4x = 16

Reorder the terms:
6(-2 + x) * 4x = 16

Reorder the terms for easier multiplication:
6 * 4x(-2 + x) = 16

Multiply 6 * 4
24x(-2 + x) = 16
(-2 * 24x + x * 24x) = 16
(-48x + 24x2) = 16

Solving
-48x + 24x2 = 16

Solving for variable 'x'.

Reorder the terms:
-16 + -48x + 24x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + -48x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-2 + -6x + 3x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-2 + -6x + 3x2)' equal to zero and attempt to solve:

Simplifying
-2 + -6x + 3x2 = 0

Solving
-2 + -6x + 3x2 = 0

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

Divide each side by '3'.
-0.6666666667 + -2x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -2x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -2x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -2x + x2 = 0 + 0.6666666667
-2x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-2x + x2 = 0.6666666667

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 = 0.6666666667 + 1

Reorder the terms:
1 + -2x + x2 = 0.6666666667 + 1

Combine like terms: 0.6666666667 + 1 = 1.6666666667
1 + -2x + x2 = 1.6666666667

Factor a perfect square on the left side:
(x + -1)(x + -1) = 1.6666666667

Calculate the square root of the right side: 1.290994449

Break this problem into two subproblems by setting 
(x + -1) equal to 1.290994449 and -1.290994449.

Subproblem 1
x + -1 = 1.290994449

Simplifying
x + -1 = 1.290994449

Reorder the terms:
-1 + x = 1.290994449

Solving
-1 + x = 1.290994449

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 = 1.290994449 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.290994449 + 1
x = 1.290994449 + 1

Combine like terms: 1.290994449 + 1 = 2.290994449
x = 2.290994449

Simplifying
x = 2.290994449

Subproblem 2
x + -1 = -1.290994449

Simplifying
x + -1 = -1.290994449

Reorder the terms:
-1 + x = -1.290994449

Solving
-1 + x = -1.290994449

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 = -1.290994449 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.290994449 + 1
x = -1.290994449 + 1

Combine like terms: -1.290994449 + 1 = -0.290994449
x = -0.290994449

Simplifying
x = -0.290994449

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.290994449, -0.290994449}
Solution
x = {2.290994449, -0.290994449}