12x(x-1)=8x+12

Solution for 12x(x-1)=8x+12 equation:

Simplifying
12x(x + -1) = 8x + 12

Reorder the terms:
12x(-1 + x) = 8x + 12
(-1 * 12x + x * 12x) = 8x + 12
(-12x + 12x2) = 8x + 12

Reorder the terms:
-12x + 12x2 = 12 + 8x

Solving
-12x + 12x2 = 12 + 8x

Solving for variable 'x'.

Reorder the terms:
-12 + -12x + -8x + 12x2 = 12 + 8x + -12 + -8x

Combine like terms: -12x + -8x = -20x
-12 + -20x + 12x2 = 12 + 8x + -12 + -8x

Reorder the terms:
-12 + -20x + 12x2 = 12 + -12 + 8x + -8x

Combine like terms: 12 + -12 = 0
-12 + -20x + 12x2 = 0 + 8x + -8x
-12 + -20x + 12x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-12 + -20x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + -5x + 3x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-3 + -5x + 3x2)' equal to zero and attempt to solve:

Simplifying
-3 + -5x + 3x2 = 0

Solving
-3 + -5x + 3x2 = 0

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

Divide each side by '3'.
-1 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1.666666667x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -1.666666667x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1.666666667x + x2 = 0 + 1
-1.666666667x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1.666666667x + x2 = 1

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = 1 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = 1 + 0.6944444447

Combine like terms: 1 + 0.6944444447 = 1.6944444447
0.6944444447 + -1.666666667x + x2 = 1.6944444447

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 1.6944444447

Calculate the square root of the right side: 1.301708279

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 1.301708279 and -1.301708279.

Subproblem 1
x + -0.8333333335 = 1.301708279

Simplifying
x + -0.8333333335 = 1.301708279

Reorder the terms:
-0.8333333335 + x = 1.301708279

Solving
-0.8333333335 + x = 1.301708279

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = 1.301708279 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = 1.301708279 + 0.8333333335
x = 1.301708279 + 0.8333333335

Combine like terms: 1.301708279 + 0.8333333335 = 2.1350416125
x = 2.1350416125

Simplifying
x = 2.1350416125

Subproblem 2
x + -0.8333333335 = -1.301708279

Simplifying
x + -0.8333333335 = -1.301708279

Reorder the terms:
-0.8333333335 + x = -1.301708279

Solving
-0.8333333335 + x = -1.301708279

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = -1.301708279 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = -1.301708279 + 0.8333333335
x = -1.301708279 + 0.8333333335

Combine like terms: -1.301708279 + 0.8333333335 = -0.4683749455
x = -0.4683749455

Simplifying
x = -0.4683749455

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.1350416125, -0.4683749455}
Solution
x = {2.1350416125, -0.4683749455}