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

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

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

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

Remove parenthesis around (2x)
-2x + -6x2 = -4 * 2x + -4

Multiply -4 * 2
-2x + -6x2 = -8x + -4

Reorder the terms:
-2x + -6x2 = -4 + -8x

Solving
-2x + -6x2 = -4 + -8x

Solving for variable 'x'.

Reorder the terms:
4 + -2x + 8x + -6x2 = -4 + -8x + 4 + 8x

Combine like terms: -2x + 8x = 6x
4 + 6x + -6x2 = -4 + -8x + 4 + 8x

Reorder the terms:
4 + 6x + -6x2 = -4 + 4 + -8x + 8x

Combine like terms: -4 + 4 = 0
4 + 6x + -6x2 = 0 + -8x + 8x
4 + 6x + -6x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
4 + 6x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 3x + -3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + 3x + -3x2)' equal to zero and attempt to solve:

Simplifying
2 + 3x + -3x2 = 0

Solving
2 + 3x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-0.6666666667 + -1x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -1x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -1x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -1x + x2 = 0 + 0.6666666667
-1x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-1x + x2 = 0.6666666667

The x term is -1x.  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.
-1x + 0.25 + x2 = 0.6666666667 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 0.6666666667 + 0.25

Combine like terms: 0.6666666667 + 0.25 = 0.9166666667
0.25 + -1x + x2 = 0.9166666667

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.9166666667

Calculate the square root of the right side: 0.957427108

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.957427108 and -0.957427108.

Subproblem 1
x + -0.5 = 0.957427108

Simplifying
x + -0.5 = 0.957427108

Reorder the terms:
-0.5 + x = 0.957427108

Solving
-0.5 + x = 0.957427108

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 = 0.957427108 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.957427108 + 0.5
x = 0.957427108 + 0.5

Combine like terms: 0.957427108 + 0.5 = 1.457427108
x = 1.457427108

Simplifying
x = 1.457427108

Subproblem 2
x + -0.5 = -0.957427108

Simplifying
x + -0.5 = -0.957427108

Reorder the terms:
-0.5 + x = -0.957427108

Solving
-0.5 + x = -0.957427108

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 = -0.957427108 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -0.957427108 + 0.5
x = -0.957427108 + 0.5

Combine like terms: -0.957427108 + 0.5 = -0.457427108
x = -0.457427108

Simplifying
x = -0.457427108

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.457427108, -0.457427108}
Solution
x = {1.457427108, -0.457427108}