12x^2-160x+60=0

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Solution for 12x^2-160x+60=0 equation: 


Simplifying
12x2 + -160x + 60 = 0

Reorder the terms:
60 + -160x + 12x2 = 0

Solving
60 + -160x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(15 + -40x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(15 + -40x + 3x2)' equal to zero and attempt to solve:

Simplifying
15 + -40x + 3x2 = 0

Solving
15 + -40x + 3x2 = 0

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

Divide each side by '3'.
5 + -13.33333333x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -13.33333333x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -13.33333333x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -13.33333333x + x2 = 0 + -5
-13.33333333x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-13.33333333x + x2 = -5

The x term is -13.33333333x.  Take half its coefficient (-6.666666665).
Square it (44.44444442) and add it to both sides.

Add '44.44444442' to each side of the equation.
-13.33333333x + 44.44444442 + x2 = -5 + 44.44444442

Reorder the terms:
44.44444442 + -13.33333333x + x2 = -5 + 44.44444442

Combine like terms: -5 + 44.44444442 = 39.44444442
44.44444442 + -13.33333333x + x2 = 39.44444442

Factor a perfect square on the left side:
(x + -6.666666665)(x + -6.666666665) = 39.44444442

Calculate the square root of the right side: 6.280481225

Break this problem into two subproblems by setting 
(x + -6.666666665) equal to 6.280481225 and -6.280481225.


Subproblem 1
x + -6.666666665 = 6.280481225

Simplifying
x + -6.666666665 = 6.280481225

Reorder the terms:
-6.666666665 + x = 6.280481225

Solving
-6.666666665 + x = 6.280481225

Solving for variable 'x'.

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

Add '6.666666665' to each side of the equation.
-6.666666665 + 6.666666665 + x = 6.280481225 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + x = 6.280481225 + 6.666666665
x = 6.280481225 + 6.666666665

Combine like terms: 6.280481225 + 6.666666665 = 12.94714789
x = 12.94714789

Simplifying
x = 12.94714789


Subproblem 2
x + -6.666666665 = -6.280481225

Simplifying
x + -6.666666665 = -6.280481225

Reorder the terms:
-6.666666665 + x = -6.280481225

Solving
-6.666666665 + x = -6.280481225

Solving for variable 'x'.

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

Add '6.666666665' to each side of the equation.
-6.666666665 + 6.666666665 + x = -6.280481225 + 6.666666665

Combine like terms: -6.666666665 + 6.666666665 = 0.000000000
0.000000000 + x = -6.280481225 + 6.666666665
x = -6.280481225 + 6.666666665

Combine like terms: -6.280481225 + 6.666666665 = 0.38618544
x = 0.38618544

Simplifying
x = 0.38618544


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.94714789, 0.38618544}
Solution
x = {12.94714789, 0.38618544}

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