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

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

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

Reorder the terms:
-6x(-4 + 3x) = 4x + -2(x + 2)
(-4 * -6x + 3x * -6x) = 4x + -2(x + 2)
(24x + -18x2) = 4x + -2(x + 2)

Reorder the terms:
24x + -18x2 = 4x + -2(2 + x)
24x + -18x2 = 4x + (2 * -2 + x * -2)
24x + -18x2 = 4x + (-4 + -2x)

Reorder the terms:
24x + -18x2 = -4 + 4x + -2x

Combine like terms: 4x + -2x = 2x
24x + -18x2 = -4 + 2x

Solving
24x + -18x2 = -4 + 2x

Solving for variable 'x'.

Reorder the terms:
4 + 24x + -2x + -18x2 = -4 + 2x + 4 + -2x

Combine like terms: 24x + -2x = 22x
4 + 22x + -18x2 = -4 + 2x + 4 + -2x

Reorder the terms:
4 + 22x + -18x2 = -4 + 4 + 2x + -2x

Combine like terms: -4 + 4 = 0
4 + 22x + -18x2 = 0 + 2x + -2x
4 + 22x + -18x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
4 + 22x + -18x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 11x + -9x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + 11x + -9x2)' equal to zero and attempt to solve:

Simplifying
2 + 11x + -9x2 = 0

Solving
2 + 11x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-0.2222222222 + -1.222222222x + x2 = 0

Move the constant term to the right:

Add '0.2222222222' to each side of the equation.
-0.2222222222 + -1.222222222x + 0.2222222222 + x2 = 0 + 0.2222222222

Reorder the terms:
-0.2222222222 + 0.2222222222 + -1.222222222x + x2 = 0 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + -1.222222222x + x2 = 0 + 0.2222222222
-1.222222222x + x2 = 0 + 0.2222222222

Combine like terms: 0 + 0.2222222222 = 0.2222222222
-1.222222222x + x2 = 0.2222222222

The x term is -1.222222222x.  Take half its coefficient (-0.611111111).
Square it (0.3734567900) and add it to both sides.

Add '0.3734567900' to each side of the equation.
-1.222222222x + 0.3734567900 + x2 = 0.2222222222 + 0.3734567900

Reorder the terms:
0.3734567900 + -1.222222222x + x2 = 0.2222222222 + 0.3734567900

Combine like terms: 0.2222222222 + 0.3734567900 = 0.5956790122
0.3734567900 + -1.222222222x + x2 = 0.5956790122

Factor a perfect square on the left side:
(x + -0.611111111)(x + -0.611111111) = 0.5956790122

Calculate the square root of the right side: 0.771802444

Break this problem into two subproblems by setting 
(x + -0.611111111) equal to 0.771802444 and -0.771802444.

Subproblem 1
x + -0.611111111 = 0.771802444

Simplifying
x + -0.611111111 = 0.771802444

Reorder the terms:
-0.611111111 + x = 0.771802444

Solving
-0.611111111 + x = 0.771802444

Solving for variable 'x'.

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

Add '0.611111111' to each side of the equation.
-0.611111111 + 0.611111111 + x = 0.771802444 + 0.611111111

Combine like terms: -0.611111111 + 0.611111111 = 0.000000000
0.000000000 + x = 0.771802444 + 0.611111111
x = 0.771802444 + 0.611111111

Combine like terms: 0.771802444 + 0.611111111 = 1.382913555
x = 1.382913555

Simplifying
x = 1.382913555

Subproblem 2
x + -0.611111111 = -0.771802444

Simplifying
x + -0.611111111 = -0.771802444

Reorder the terms:
-0.611111111 + x = -0.771802444

Solving
-0.611111111 + x = -0.771802444

Solving for variable 'x'.

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

Add '0.611111111' to each side of the equation.
-0.611111111 + 0.611111111 + x = -0.771802444 + 0.611111111

Combine like terms: -0.611111111 + 0.611111111 = 0.000000000
0.000000000 + x = -0.771802444 + 0.611111111
x = -0.771802444 + 0.611111111

Combine like terms: -0.771802444 + 0.611111111 = -0.160691333
x = -0.160691333

Simplifying
x = -0.160691333

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.382913555, -0.160691333}
Solution
x = {1.382913555, -0.160691333}