-6x-2(-3x-1)(-3x-1)=0

Solution for -6x-2(-3x-1)(-3x-1)=0 equation:

Simplifying
-6x + -2(-3x + -1)(-3x + -1) = 0

Reorder the terms:
-6x + -2(-1 + -3x)(-3x + -1) = 0

Reorder the terms:
-6x + -2(-1 + -3x)(-1 + -3x) = 0

Multiply (-1 + -3x) * (-1 + -3x)
-6x + -2(-1(-1 + -3x) + -3x * (-1 + -3x)) = 0
-6x + -2((-1 * -1 + -3x * -1) + -3x * (-1 + -3x)) = 0
-6x + -2((1 + 3x) + -3x * (-1 + -3x)) = 0
-6x + -2(1 + 3x + (-1 * -3x + -3x * -3x)) = 0
-6x + -2(1 + 3x + (3x + 9x2)) = 0

Combine like terms: 3x + 3x = 6x
-6x + -2(1 + 6x + 9x2) = 0
-6x + (1 * -2 + 6x * -2 + 9x2 * -2) = 0
-6x + (-2 + -12x + -18x2) = 0

Reorder the terms:
-2 + -6x + -12x + -18x2 = 0

Combine like terms: -6x + -12x = -18x
-2 + -18x + -18x2 = 0

Solving
-2 + -18x + -18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(1 + 9x + 9x2) = 0

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

Simplifying
1 + 9x + 9x2 = 0

Solving
1 + 9x + 9x2 = 0

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

Divide each side by '9'.
0.1111111111 + x + x2 = 0

Move the constant term to the right:

Add '-0.1111111111' to each side of the equation.
0.1111111111 + x + -0.1111111111 + x2 = 0 + -0.1111111111

Reorder the terms:
0.1111111111 + -0.1111111111 + x + x2 = 0 + -0.1111111111

Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000
0.0000000000 + x + x2 = 0 + -0.1111111111
x + x2 = 0 + -0.1111111111

Combine like terms: 0 + -0.1111111111 = -0.1111111111
x + x2 = -0.1111111111

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = -0.1111111111 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = -0.1111111111 + 0.25

Combine like terms: -0.1111111111 + 0.25 = 0.1388888889
1.25 + x2 = 0.1388888889

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.1388888889

Calculate the square root of the right side: 0.372677996

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.372677996 and -0.372677996.

Subproblem 1
x + 0.5 = 0.372677996

Simplifying
x + 0.5 = 0.372677996

Reorder the terms:
0.5 + x = 0.372677996

Solving
0.5 + x = 0.372677996

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 0.372677996 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.372677996 + -0.5
x = 0.372677996 + -0.5

Combine like terms: 0.372677996 + -0.5 = -0.127322004
x = -0.127322004

Simplifying
x = -0.127322004

Subproblem 2
x + 0.5 = -0.372677996

Simplifying
x + 0.5 = -0.372677996

Reorder the terms:
0.5 + x = -0.372677996

Solving
0.5 + x = -0.372677996

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -0.372677996 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.372677996 + -0.5
x = -0.372677996 + -0.5

Combine like terms: -0.372677996 + -0.5 = -0.872677996
x = -0.872677996

Simplifying
x = -0.872677996

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.127322004, -0.872677996}
Solution
x = {-0.127322004, -0.872677996}