6x(-2x-6)-(4x-2)=(-2)(3x+1)

Solution for 6x(-2x-6)-(4x-2)=(-2)(3x+1) equation:

Simplifying
6x(-2x + -6) + -1(4x + -2) = (-2)(3x + 1)

Reorder the terms:
6x(-6 + -2x) + -1(4x + -2) = (-2)(3x + 1)
(-6 * 6x + -2x * 6x) + -1(4x + -2) = (-2)(3x + 1)
(-36x + -12x2) + -1(4x + -2) = (-2)(3x + 1)

Reorder the terms:
-36x + -12x2 + -1(-2 + 4x) = (-2)(3x + 1)
-36x + -12x2 + (-2 * -1 + 4x * -1) = (-2)(3x + 1)
-36x + -12x2 + (2 + -4x) = (-2)(3x + 1)

Reorder the terms:
2 + -36x + -4x + -12x2 = (-2)(3x + 1)

Combine like terms: -36x + -4x = -40x
2 + -40x + -12x2 = (-2)(3x + 1)

Reorder the terms:
2 + -40x + -12x2 = -2(1 + 3x)
2 + -40x + -12x2 = (1 * -2 + 3x * -2)
2 + -40x + -12x2 = (-2 + -6x)

Solving
2 + -40x + -12x2 = -2 + -6x

Solving for variable 'x'.

Reorder the terms:
2 + 2 + -40x + 6x + -12x2 = -2 + -6x + 2 + 6x

Combine like terms: 2 + 2 = 4
4 + -40x + 6x + -12x2 = -2 + -6x + 2 + 6x

Combine like terms: -40x + 6x = -34x
4 + -34x + -12x2 = -2 + -6x + 2 + 6x

Reorder the terms:
4 + -34x + -12x2 = -2 + 2 + -6x + 6x

Combine like terms: -2 + 2 = 0
4 + -34x + -12x2 = 0 + -6x + 6x
4 + -34x + -12x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
4 + -34x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -17x + -6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + -17x + -6x2)' equal to zero and attempt to solve:

Simplifying
2 + -17x + -6x2 = 0

Solving
2 + -17x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-0.3333333333 + 2.833333333x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 2.833333333x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 2.833333333x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 2.833333333x + x2 = 0 + 0.3333333333
2.833333333x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
2.833333333x + x2 = 0.3333333333

The x term is 2.833333333x.  Take half its coefficient (1.416666667).
Square it (2.006944445) and add it to both sides.

Add '2.006944445' to each side of the equation.
2.833333333x + 2.006944445 + x2 = 0.3333333333 + 2.006944445

Reorder the terms:
2.006944445 + 2.833333333x + x2 = 0.3333333333 + 2.006944445

Combine like terms: 0.3333333333 + 2.006944445 = 2.3402777783
2.006944445 + 2.833333333x + x2 = 2.3402777783

Factor a perfect square on the left side:
(x + 1.416666667)(x + 1.416666667) = 2.3402777783

Calculate the square root of the right side: 1.529796646

Break this problem into two subproblems by setting 
(x + 1.416666667) equal to 1.529796646 and -1.529796646.

Subproblem 1
x + 1.416666667 = 1.529796646

Simplifying
x + 1.416666667 = 1.529796646

Reorder the terms:
1.416666667 + x = 1.529796646

Solving
1.416666667 + x = 1.529796646

Solving for variable 'x'.

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

Add '-1.416666667' to each side of the equation.
1.416666667 + -1.416666667 + x = 1.529796646 + -1.416666667

Combine like terms: 1.416666667 + -1.416666667 = 0.000000000
0.000000000 + x = 1.529796646 + -1.416666667
x = 1.529796646 + -1.416666667

Combine like terms: 1.529796646 + -1.416666667 = 0.113129979
x = 0.113129979

Simplifying
x = 0.113129979

Subproblem 2
x + 1.416666667 = -1.529796646

Simplifying
x + 1.416666667 = -1.529796646

Reorder the terms:
1.416666667 + x = -1.529796646

Solving
1.416666667 + x = -1.529796646

Solving for variable 'x'.

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

Add '-1.416666667' to each side of the equation.
1.416666667 + -1.416666667 + x = -1.529796646 + -1.416666667

Combine like terms: 1.416666667 + -1.416666667 = 0.000000000
0.000000000 + x = -1.529796646 + -1.416666667
x = -1.529796646 + -1.416666667

Combine like terms: -1.529796646 + -1.416666667 = -2.946463313
x = -2.946463313

Simplifying
x = -2.946463313

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.113129979, -2.946463313}
Solution
x = {0.113129979, -2.946463313}