2x-12(x-12)(x+4)=250

Solution for 2x-12(x-12)(x+4)=250 equation:

Simplifying
2x + -12(x + -12)(x + 4) = 250

Reorder the terms:
2x + -12(-12 + x)(x + 4) = 250

Reorder the terms:
2x + -12(-12 + x)(4 + x) = 250

Multiply (-12 + x) * (4 + x)
2x + -12(-12(4 + x) + x(4 + x)) = 250
2x + -12((4 * -12 + x * -12) + x(4 + x)) = 250
2x + -12((-48 + -12x) + x(4 + x)) = 250
2x + -12(-48 + -12x + (4 * x + x * x)) = 250
2x + -12(-48 + -12x + (4x + x2)) = 250

Combine like terms: -12x + 4x = -8x
2x + -12(-48 + -8x + x2) = 250
2x + (-48 * -12 + -8x * -12 + x2 * -12) = 250
2x + (576 + 96x + -12x2) = 250

Reorder the terms:
576 + 2x + 96x + -12x2 = 250

Combine like terms: 2x + 96x = 98x
576 + 98x + -12x2 = 250

Solving
576 + 98x + -12x2 = 250

Solving for variable 'x'.

Reorder the terms:
576 + -250 + 98x + -12x2 = 250 + -250

Combine like terms: 576 + -250 = 326
326 + 98x + -12x2 = 250 + -250

Combine like terms: 250 + -250 = 0
326 + 98x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(163 + 49x + -6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(163 + 49x + -6x2)' equal to zero and attempt to solve:

Simplifying
163 + 49x + -6x2 = 0

Solving
163 + 49x + -6x2 = 0

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

Divide each side by '-6'.
-27.16666667 + -8.166666667x + x2 = 0

Move the constant term to the right:

Add '27.16666667' to each side of the equation.
-27.16666667 + -8.166666667x + 27.16666667 + x2 = 0 + 27.16666667

Reorder the terms:
-27.16666667 + 27.16666667 + -8.166666667x + x2 = 0 + 27.16666667

Combine like terms: -27.16666667 + 27.16666667 = 0.00000000
0.00000000 + -8.166666667x + x2 = 0 + 27.16666667
-8.166666667x + x2 = 0 + 27.16666667

Combine like terms: 0 + 27.16666667 = 27.16666667
-8.166666667x + x2 = 27.16666667

The x term is -8.166666667x.  Take half its coefficient (-4.083333334).
Square it (16.67361112) and add it to both sides.

Add '16.67361112' to each side of the equation.
-8.166666667x + 16.67361112 + x2 = 27.16666667 + 16.67361112

Reorder the terms:
16.67361112 + -8.166666667x + x2 = 27.16666667 + 16.67361112

Combine like terms: 27.16666667 + 16.67361112 = 43.84027779
16.67361112 + -8.166666667x + x2 = 43.84027779

Factor a perfect square on the left side:
(x + -4.083333334)(x + -4.083333334) = 43.84027779

Calculate the square root of the right side: 6.62119912

Break this problem into two subproblems by setting 
(x + -4.083333334) equal to 6.62119912 and -6.62119912.

Subproblem 1
x + -4.083333334 = 6.62119912

Simplifying
x + -4.083333334 = 6.62119912

Reorder the terms:
-4.083333334 + x = 6.62119912

Solving
-4.083333334 + x = 6.62119912

Solving for variable 'x'.

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

Add '4.083333334' to each side of the equation.
-4.083333334 + 4.083333334 + x = 6.62119912 + 4.083333334

Combine like terms: -4.083333334 + 4.083333334 = 0.000000000
0.000000000 + x = 6.62119912 + 4.083333334
x = 6.62119912 + 4.083333334

Combine like terms: 6.62119912 + 4.083333334 = 10.704532454
x = 10.704532454

Simplifying
x = 10.704532454

Subproblem 2
x + -4.083333334 = -6.62119912

Simplifying
x + -4.083333334 = -6.62119912

Reorder the terms:
-4.083333334 + x = -6.62119912

Solving
-4.083333334 + x = -6.62119912

Solving for variable 'x'.

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

Add '4.083333334' to each side of the equation.
-4.083333334 + 4.083333334 + x = -6.62119912 + 4.083333334

Combine like terms: -4.083333334 + 4.083333334 = 0.000000000
0.000000000 + x = -6.62119912 + 4.083333334
x = -6.62119912 + 4.083333334

Combine like terms: -6.62119912 + 4.083333334 = -2.537865786
x = -2.537865786

Simplifying
x = -2.537865786

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.704532454, -2.537865786}
Solution
x = {10.704532454, -2.537865786}