-2(4-3x)6x=10

Solution for -2(4-3x)6x=10 equation:

Simplifying
-2(4 + -3x) * 6x = 10

Reorder the terms for easier multiplication:
-2 * 6x(4 + -3x) = 10

Multiply -2 * 6
-12x(4 + -3x) = 10
(4 * -12x + -3x * -12x) = 10
(-48x + 36x2) = 10

Solving
-48x + 36x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + -48x + 36x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -48x + 36x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -24x + 18x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -24x + 18x2)' equal to zero and attempt to solve:

Simplifying
-5 + -24x + 18x2 = 0

Solving
-5 + -24x + 18x2 = 0

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

Divide each side by '18'.
-0.2777777778 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '0.2777777778' to each side of the equation.
-0.2777777778 + -1.333333333x + 0.2777777778 + x2 = 0 + 0.2777777778

Reorder the terms:
-0.2777777778 + 0.2777777778 + -1.333333333x + x2 = 0 + 0.2777777778

Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000
0.0000000000 + -1.333333333x + x2 = 0 + 0.2777777778
-1.333333333x + x2 = 0 + 0.2777777778

Combine like terms: 0 + 0.2777777778 = 0.2777777778
-1.333333333x + x2 = 0.2777777778

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 0.2777777778 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 0.2777777778 + 0.4444444442

Combine like terms: 0.2777777778 + 0.4444444442 = 0.722222222
0.4444444442 + -1.333333333x + x2 = 0.722222222

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 0.722222222

Calculate the square root of the right side: 0.849836585

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 0.849836585 and -0.849836585.

Subproblem 1
x + -0.6666666665 = 0.849836585

Simplifying
x + -0.6666666665 = 0.849836585

Reorder the terms:
-0.6666666665 + x = 0.849836585

Solving
-0.6666666665 + x = 0.849836585

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = 0.849836585 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 0.849836585 + 0.6666666665
x = 0.849836585 + 0.6666666665

Combine like terms: 0.849836585 + 0.6666666665 = 1.5165032515
x = 1.5165032515

Simplifying
x = 1.5165032515

Subproblem 2
x + -0.6666666665 = -0.849836585

Simplifying
x + -0.6666666665 = -0.849836585

Reorder the terms:
-0.6666666665 + x = -0.849836585

Solving
-0.6666666665 + x = -0.849836585

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = -0.849836585 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -0.849836585 + 0.6666666665
x = -0.849836585 + 0.6666666665

Combine like terms: -0.849836585 + 0.6666666665 = -0.1831699185
x = -0.1831699185

Simplifying
x = -0.1831699185

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5165032515, -0.1831699185}
Solution
x = {1.5165032515, -0.1831699185}