=12x^2-560x+4000

Solution for =12x^2-560x+4000 equation:

Simplifying
0 = 12x2 + -560x + 4000

Reorder the terms:
0 = 4000 + -560x + 12x2

Solving
0 = 4000 + -560x + 12x2

Solving for variable 'x'.

Combine like terms: 0 + -4000 = -4000
-4000 + 560x + -12x2 = 4000 + -560x + 12x2 + -4000 + 560x + -12x2

Reorder the terms:
-4000 + 560x + -12x2 = 4000 + -4000 + -560x + 560x + 12x2 + -12x2

Combine like terms: 4000 + -4000 = 0
-4000 + 560x + -12x2 = 0 + -560x + 560x + 12x2 + -12x2
-4000 + 560x + -12x2 = -560x + 560x + 12x2 + -12x2

Combine like terms: -560x + 560x = 0
-4000 + 560x + -12x2 = 0 + 12x2 + -12x2
-4000 + 560x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-4000 + 560x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1000 + 140x + -3x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1000 + 140x + -3x2)' equal to zero and attempt to solve:

Simplifying
-1000 + 140x + -3x2 = 0

Solving
-1000 + 140x + -3x2 = 0

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

Divide each side by '-3'.
333.3333333 + -46.66666667x + x2 = 0

Move the constant term to the right:

Add '-333.3333333' to each side of the equation.
333.3333333 + -46.66666667x + -333.3333333 + x2 = 0 + -333.3333333

Reorder the terms:
333.3333333 + -333.3333333 + -46.66666667x + x2 = 0 + -333.3333333

Combine like terms: 333.3333333 + -333.3333333 = 0.0000000
0.0000000 + -46.66666667x + x2 = 0 + -333.3333333
-46.66666667x + x2 = 0 + -333.3333333

Combine like terms: 0 + -333.3333333 = -333.3333333
-46.66666667x + x2 = -333.3333333

The x term is -46.66666667x.  Take half its coefficient (-23.33333334).
Square it (544.4444448) and add it to both sides.

Add '544.4444448' to each side of the equation.
-46.66666667x + 544.4444448 + x2 = -333.3333333 + 544.4444448

Reorder the terms:
544.4444448 + -46.66666667x + x2 = -333.3333333 + 544.4444448

Combine like terms: -333.3333333 + 544.4444448 = 211.1111115
544.4444448 + -46.66666667x + x2 = 211.1111115

Factor a perfect square on the left side:
(x + -23.33333334)(x + -23.33333334) = 211.1111115

Calculate the square root of the right side: 14.529663159

Break this problem into two subproblems by setting 
(x + -23.33333334) equal to 14.529663159 and -14.529663159.

Subproblem 1
x + -23.33333334 = 14.529663159

Simplifying
x + -23.33333334 = 14.529663159

Reorder the terms:
-23.33333334 + x = 14.529663159

Solving
-23.33333334 + x = 14.529663159

Solving for variable 'x'.

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

Add '23.33333334' to each side of the equation.
-23.33333334 + 23.33333334 + x = 14.529663159 + 23.33333334

Combine like terms: -23.33333334 + 23.33333334 = 0.00000000
0.00000000 + x = 14.529663159 + 23.33333334
x = 14.529663159 + 23.33333334

Combine like terms: 14.529663159 + 23.33333334 = 37.862996499
x = 37.862996499

Simplifying
x = 37.862996499

Subproblem 2
x + -23.33333334 = -14.529663159

Simplifying
x + -23.33333334 = -14.529663159

Reorder the terms:
-23.33333334 + x = -14.529663159

Solving
-23.33333334 + x = -14.529663159

Solving for variable 'x'.

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

Add '23.33333334' to each side of the equation.
-23.33333334 + 23.33333334 + x = -14.529663159 + 23.33333334

Combine like terms: -23.33333334 + 23.33333334 = 0.00000000
0.00000000 + x = -14.529663159 + 23.33333334
x = -14.529663159 + 23.33333334

Combine like terms: -14.529663159 + 23.33333334 = 8.803670181
x = 8.803670181

Simplifying
x = 8.803670181

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {37.862996499, 8.803670181}
Solution
x = {37.862996499, 8.803670181}