12x^2-128x+240=0

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Solution for 12x^2-128x+240=0 equation: 


Simplifying
12x2 + -128x + 240 = 0

Reorder the terms:
240 + -128x + 12x2 = 0

Solving
240 + -128x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(60 + -32x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(60 + -32x + 3x2)' equal to zero and attempt to solve:

Simplifying
60 + -32x + 3x2 = 0

Solving
60 + -32x + 3x2 = 0

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

Divide each side by '3'.
20 + -10.66666667x + x2 = 0

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -10.66666667x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + -10.66666667x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -10.66666667x + x2 = 0 + -20
-10.66666667x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
-10.66666667x + x2 = -20

The x term is -10.66666667x.  Take half its coefficient (-5.333333335).
Square it (28.44444446) and add it to both sides.

Add '28.44444446' to each side of the equation.
-10.66666667x + 28.44444446 + x2 = -20 + 28.44444446

Reorder the terms:
28.44444446 + -10.66666667x + x2 = -20 + 28.44444446

Combine like terms: -20 + 28.44444446 = 8.44444446
28.44444446 + -10.66666667x + x2 = 8.44444446

Factor a perfect square on the left side:
(x + -5.333333335)(x + -5.333333335) = 8.44444446

Calculate the square root of the right side: 2.905932632

Break this problem into two subproblems by setting 
(x + -5.333333335) equal to 2.905932632 and -2.905932632.


Subproblem 1
x + -5.333333335 = 2.905932632

Simplifying
x + -5.333333335 = 2.905932632

Reorder the terms:
-5.333333335 + x = 2.905932632

Solving
-5.333333335 + x = 2.905932632

Solving for variable 'x'.

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

Add '5.333333335' to each side of the equation.
-5.333333335 + 5.333333335 + x = 2.905932632 + 5.333333335

Combine like terms: -5.333333335 + 5.333333335 = 0.000000000
0.000000000 + x = 2.905932632 + 5.333333335
x = 2.905932632 + 5.333333335

Combine like terms: 2.905932632 + 5.333333335 = 8.239265967
x = 8.239265967

Simplifying
x = 8.239265967


Subproblem 2
x + -5.333333335 = -2.905932632

Simplifying
x + -5.333333335 = -2.905932632

Reorder the terms:
-5.333333335 + x = -2.905932632

Solving
-5.333333335 + x = -2.905932632

Solving for variable 'x'.

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

Add '5.333333335' to each side of the equation.
-5.333333335 + 5.333333335 + x = -2.905932632 + 5.333333335

Combine like terms: -5.333333335 + 5.333333335 = 0.000000000
0.000000000 + x = -2.905932632 + 5.333333335
x = -2.905932632 + 5.333333335

Combine like terms: -2.905932632 + 5.333333335 = 2.427400703
x = 2.427400703

Simplifying
x = 2.427400703


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.239265967, 2.427400703}
Solution
x = {8.239265967, 2.427400703}

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