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

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

Simplifying
-2x(4 + 3x) = -6 + -4x
(4 * -2x + 3x * -2x) = -6 + -4x
(-8x + -6x2) = -6 + -4x

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

Solving for variable 'x'.

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

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

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

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

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

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

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

Simplifying
3 + -2x + -3x2 = 0

Solving
3 + -2x + -3x2 = 0

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

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

Move the constant term to the right:

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

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

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

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

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 1 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 1 + 0.1111111112

Combine like terms: 1 + 0.1111111112 = 1.1111111112
0.1111111112 + 0.6666666667x + x2 = 1.1111111112

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 1.1111111112

Calculate the square root of the right side: 1.054092553

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 1.054092553 and -1.054092553.

Subproblem 1
x + 0.3333333334 = 1.054092553

Simplifying
x + 0.3333333334 = 1.054092553

Reorder the terms:
0.3333333334 + x = 1.054092553

Solving
0.3333333334 + x = 1.054092553

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 1.054092553 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 1.054092553 + -0.3333333334
x = 1.054092553 + -0.3333333334

Combine like terms: 1.054092553 + -0.3333333334 = 0.7207592196
x = 0.7207592196

Simplifying
x = 0.7207592196

Subproblem 2
x + 0.3333333334 = -1.054092553

Simplifying
x + 0.3333333334 = -1.054092553

Reorder the terms:
0.3333333334 + x = -1.054092553

Solving
0.3333333334 + x = -1.054092553

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -1.054092553 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -1.054092553 + -0.3333333334
x = -1.054092553 + -0.3333333334

Combine like terms: -1.054092553 + -0.3333333334 = -1.3874258864
x = -1.3874258864

Simplifying
x = -1.3874258864

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.7207592196, -1.3874258864}
Solution
x = {0.7207592196, -1.3874258864}