12x^2-144x+320=0

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Solution for 12x^2-144x+320=0 equation: 


Simplifying
12x2 + -144x + 320 = 0

Reorder the terms:
320 + -144x + 12x2 = 0

Solving
320 + -144x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(80 + -36x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(80 + -36x + 3x2)' equal to zero and attempt to solve:

Simplifying
80 + -36x + 3x2 = 0

Solving
80 + -36x + 3x2 = 0

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

Divide each side by '3'.
26.66666667 + -12x + x2 = 0

Move the constant term to the right:

Add '-26.66666667' to each side of the equation.
26.66666667 + -12x + -26.66666667 + x2 = 0 + -26.66666667

Reorder the terms:
26.66666667 + -26.66666667 + -12x + x2 = 0 + -26.66666667

Combine like terms: 26.66666667 + -26.66666667 = 0.00000000
0.00000000 + -12x + x2 = 0 + -26.66666667
-12x + x2 = 0 + -26.66666667

Combine like terms: 0 + -26.66666667 = -26.66666667
-12x + x2 = -26.66666667

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -26.66666667 + 36

Reorder the terms:
36 + -12x + x2 = -26.66666667 + 36

Combine like terms: -26.66666667 + 36 = 9.33333333
36 + -12x + x2 = 9.33333333

Factor a perfect square on the left side:
(x + -6)(x + -6) = 9.33333333

Calculate the square root of the right side: 3.055050463

Break this problem into two subproblems by setting 
(x + -6) equal to 3.055050463 and -3.055050463.


Subproblem 1
x + -6 = 3.055050463

Simplifying
x + -6 = 3.055050463

Reorder the terms:
-6 + x = 3.055050463

Solving
-6 + x = 3.055050463

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 3.055050463 + 6

Combine like terms: -6 + 6 = 0
0 + x = 3.055050463 + 6
x = 3.055050463 + 6

Combine like terms: 3.055050463 + 6 = 9.055050463
x = 9.055050463

Simplifying
x = 9.055050463


Subproblem 2
x + -6 = -3.055050463

Simplifying
x + -6 = -3.055050463

Reorder the terms:
-6 + x = -3.055050463

Solving
-6 + x = -3.055050463

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -3.055050463 + 6

Combine like terms: -6 + 6 = 0
0 + x = -3.055050463 + 6
x = -3.055050463 + 6

Combine like terms: -3.055050463 + 6 = 2.944949537
x = 2.944949537

Simplifying
x = 2.944949537


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.055050463, 2.944949537}
Solution
x = {9.055050463, 2.944949537}

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