6(3-2x)12x=18

Solution for 6(3-2x)12x=18 equation:

Simplifying
6(3 + -2x) * 12x = 18

Reorder the terms for easier multiplication:
6 * 12x(3 + -2x) = 18

Multiply 6 * 12
72x(3 + -2x) = 18
(3 * 72x + -2x * 72x) = 18
(216x + -144x2) = 18

Solving
216x + -144x2 = 18

Solving for variable 'x'.

Reorder the terms:
-18 + 216x + -144x2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 216x + -144x2 = 0

Factor out the Greatest Common Factor (GCF), '18'.
18(-1 + 12x + -8x2) = 0

Ignore the factor 18.
Subproblem 1
Set the factor '(-1 + 12x + -8x2)' equal to zero and attempt to solve:

Simplifying
-1 + 12x + -8x2 = 0

Solving
-1 + 12x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
0.125 + -1.5x + x2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + -1.5x + -0.125 + x2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + -1.5x + x2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + -1.5x + x2 = 0 + -0.125
-1.5x + x2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
-1.5x + x2 = -0.125

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = -0.125 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = -0.125 + 0.5625

Combine like terms: -0.125 + 0.5625 = 0.4375
0.5625 + -1.5x + x2 = 0.4375

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 0.4375

Calculate the square root of the right side: 0.661437828

Break this problem into two subproblems by setting 
(x + -0.75) equal to 0.661437828 and -0.661437828.

Subproblem 1
x + -0.75 = 0.661437828

Simplifying
x + -0.75 = 0.661437828

Reorder the terms:
-0.75 + x = 0.661437828

Solving
-0.75 + x = 0.661437828

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = 0.661437828 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 0.661437828 + 0.75
x = 0.661437828 + 0.75

Combine like terms: 0.661437828 + 0.75 = 1.411437828
x = 1.411437828

Simplifying
x = 1.411437828

Subproblem 2
x + -0.75 = -0.661437828

Simplifying
x + -0.75 = -0.661437828

Reorder the terms:
-0.75 + x = -0.661437828

Solving
-0.75 + x = -0.661437828

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = -0.661437828 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -0.661437828 + 0.75
x = -0.661437828 + 0.75

Combine like terms: -0.661437828 + 0.75 = 0.088562172
x = 0.088562172

Simplifying
x = 0.088562172

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.411437828, 0.088562172}
Solution
x = {1.411437828, 0.088562172}