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

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

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

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

Reorder the terms for easier multiplication:
3 * 2x(4 + x) = 2x + -6

Multiply 3 * 2
6x(4 + x) = 2x + -6
(4 * 6x + x * 6x) = 2x + -6
(24x + 6x2) = 2x + -6

Reorder the terms:
24x + 6x2 = -6 + 2x

Solving
24x + 6x2 = -6 + 2x

Solving for variable 'x'.

Reorder the terms:
6 + 24x + -2x + 6x2 = -6 + 2x + 6 + -2x

Combine like terms: 24x + -2x = 22x
6 + 22x + 6x2 = -6 + 2x + 6 + -2x

Reorder the terms:
6 + 22x + 6x2 = -6 + 6 + 2x + -2x

Combine like terms: -6 + 6 = 0
6 + 22x + 6x2 = 0 + 2x + -2x
6 + 22x + 6x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
6 + 22x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 11x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 11x + 3x2)' equal to zero and attempt to solve:

Simplifying
3 + 11x + 3x2 = 0

Solving
3 + 11x + 3x2 = 0

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

Divide each side by '3'.
1 + 3.666666667x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 3.666666667x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 3.666666667x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3.666666667x + x2 = 0 + -1
3.666666667x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
3.666666667x + x2 = -1

The x term is 3.666666667x.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667x + 3.361111114 + x2 = -1 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667x + x2 = -1 + 3.361111114

Combine like terms: -1 + 3.361111114 = 2.361111114
3.361111114 + 3.666666667x + x2 = 2.361111114

Factor a perfect square on the left side:
(x + 1.833333334)(x + 1.833333334) = 2.361111114

Calculate the square root of the right side: 1.536590744

Break this problem into two subproblems by setting 
(x + 1.833333334) equal to 1.536590744 and -1.536590744.

Subproblem 1
x + 1.833333334 = 1.536590744

Simplifying
x + 1.833333334 = 1.536590744

Reorder the terms:
1.833333334 + x = 1.536590744

Solving
1.833333334 + x = 1.536590744

Solving for variable 'x'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + x = 1.536590744 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + x = 1.536590744 + -1.833333334
x = 1.536590744 + -1.833333334

Combine like terms: 1.536590744 + -1.833333334 = -0.29674259
x = -0.29674259

Simplifying
x = -0.29674259

Subproblem 2
x + 1.833333334 = -1.536590744

Simplifying
x + 1.833333334 = -1.536590744

Reorder the terms:
1.833333334 + x = -1.536590744

Solving
1.833333334 + x = -1.536590744

Solving for variable 'x'.

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

Add '-1.833333334' to each side of the equation.
1.833333334 + -1.833333334 + x = -1.536590744 + -1.833333334

Combine like terms: 1.833333334 + -1.833333334 = 0.000000000
0.000000000 + x = -1.536590744 + -1.833333334
x = -1.536590744 + -1.833333334

Combine like terms: -1.536590744 + -1.833333334 = -3.369924078
x = -3.369924078

Simplifying
x = -3.369924078

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.29674259, -3.369924078}
Solution
x = {-0.29674259, -3.369924078}