4x(8-3x)-12=(-2)(2+3x)

Solution for 4x(8-3x)-12=(-2)(2+3x) equation:

Simplifying
4x(8 + -3x) + -12 = (-2)(2 + 3x)
(8 * 4x + -3x * 4x) + -12 = (-2)(2 + 3x)
(32x + -12x2) + -12 = (-2)(2 + 3x)

Reorder the terms:
-12 + 32x + -12x2 = (-2)(2 + 3x)
-12 + 32x + -12x2 = (2 * -2 + 3x * -2)
-12 + 32x + -12x2 = (-4 + -6x)

Solving
-12 + 32x + -12x2 = -4 + -6x

Solving for variable 'x'.

Reorder the terms:
-12 + 4 + 32x + 6x + -12x2 = -4 + -6x + 4 + 6x

Combine like terms: -12 + 4 = -8
-8 + 32x + 6x + -12x2 = -4 + -6x + 4 + 6x

Combine like terms: 32x + 6x = 38x
-8 + 38x + -12x2 = -4 + -6x + 4 + 6x

Reorder the terms:
-8 + 38x + -12x2 = -4 + 4 + -6x + 6x

Combine like terms: -4 + 4 = 0
-8 + 38x + -12x2 = 0 + -6x + 6x
-8 + 38x + -12x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-8 + 38x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 19x + -6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + 19x + -6x2)' equal to zero and attempt to solve:

Simplifying
-4 + 19x + -6x2 = 0

Solving
-4 + 19x + -6x2 = 0

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

Divide each side by '-6'.
0.6666666667 + -3.166666667x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -3.166666667x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -3.166666667x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -3.166666667x + x2 = 0 + -0.6666666667
-3.166666667x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-3.166666667x + x2 = -0.6666666667

The x term is -3.166666667x.  Take half its coefficient (-1.583333334).
Square it (2.506944447) and add it to both sides.

Add '2.506944447' to each side of the equation.
-3.166666667x + 2.506944447 + x2 = -0.6666666667 + 2.506944447

Reorder the terms:
2.506944447 + -3.166666667x + x2 = -0.6666666667 + 2.506944447

Combine like terms: -0.6666666667 + 2.506944447 = 1.8402777803
2.506944447 + -3.166666667x + x2 = 1.8402777803

Factor a perfect square on the left side:
(x + -1.583333334)(x + -1.583333334) = 1.8402777803

Calculate the square root of the right side: 1.356568384

Break this problem into two subproblems by setting 
(x + -1.583333334) equal to 1.356568384 and -1.356568384.

Subproblem 1
x + -1.583333334 = 1.356568384

Simplifying
x + -1.583333334 = 1.356568384

Reorder the terms:
-1.583333334 + x = 1.356568384

Solving
-1.583333334 + x = 1.356568384

Solving for variable 'x'.

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

Add '1.583333334' to each side of the equation.
-1.583333334 + 1.583333334 + x = 1.356568384 + 1.583333334

Combine like terms: -1.583333334 + 1.583333334 = 0.000000000
0.000000000 + x = 1.356568384 + 1.583333334
x = 1.356568384 + 1.583333334

Combine like terms: 1.356568384 + 1.583333334 = 2.939901718
x = 2.939901718

Simplifying
x = 2.939901718

Subproblem 2
x + -1.583333334 = -1.356568384

Simplifying
x + -1.583333334 = -1.356568384

Reorder the terms:
-1.583333334 + x = -1.356568384

Solving
-1.583333334 + x = -1.356568384

Solving for variable 'x'.

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

Add '1.583333334' to each side of the equation.
-1.583333334 + 1.583333334 + x = -1.356568384 + 1.583333334

Combine like terms: -1.583333334 + 1.583333334 = 0.000000000
0.000000000 + x = -1.356568384 + 1.583333334
x = -1.356568384 + 1.583333334

Combine like terms: -1.356568384 + 1.583333334 = 0.22676495
x = 0.22676495

Simplifying
x = 0.22676495

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.939901718, 0.22676495}
Solution
x = {2.939901718, 0.22676495}