12x^2-104x+120=0

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Solution for 12x^2-104x+120=0 equation: 


Simplifying
12x2 + -104x + 120 = 0

Reorder the terms:
120 + -104x + 12x2 = 0

Solving
120 + -104x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(30 + -26x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(30 + -26x + 3x2)' equal to zero and attempt to solve:

Simplifying
30 + -26x + 3x2 = 0

Solving
30 + -26x + 3x2 = 0

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

Divide each side by '3'.
10 + -8.666666667x + x2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -8.666666667x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -8.666666667x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -8.666666667x + x2 = 0 + -10
-8.666666667x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-8.666666667x + x2 = -10

The x term is -8.666666667x.  Take half its coefficient (-4.333333334).
Square it (18.77777778) and add it to both sides.

Add '18.77777778' to each side of the equation.
-8.666666667x + 18.77777778 + x2 = -10 + 18.77777778

Reorder the terms:
18.77777778 + -8.666666667x + x2 = -10 + 18.77777778

Combine like terms: -10 + 18.77777778 = 8.77777778
18.77777778 + -8.666666667x + x2 = 8.77777778

Factor a perfect square on the left side:
(x + -4.333333334)(x + -4.333333334) = 8.77777778

Calculate the square root of the right side: 2.962731473

Break this problem into two subproblems by setting 
(x + -4.333333334) equal to 2.962731473 and -2.962731473.


Subproblem 1
x + -4.333333334 = 2.962731473

Simplifying
x + -4.333333334 = 2.962731473

Reorder the terms:
-4.333333334 + x = 2.962731473

Solving
-4.333333334 + x = 2.962731473

Solving for variable 'x'.

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

Add '4.333333334' to each side of the equation.
-4.333333334 + 4.333333334 + x = 2.962731473 + 4.333333334

Combine like terms: -4.333333334 + 4.333333334 = 0.000000000
0.000000000 + x = 2.962731473 + 4.333333334
x = 2.962731473 + 4.333333334

Combine like terms: 2.962731473 + 4.333333334 = 7.296064807
x = 7.296064807

Simplifying
x = 7.296064807


Subproblem 2
x + -4.333333334 = -2.962731473

Simplifying
x + -4.333333334 = -2.962731473

Reorder the terms:
-4.333333334 + x = -2.962731473

Solving
-4.333333334 + x = -2.962731473

Solving for variable 'x'.

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

Add '4.333333334' to each side of the equation.
-4.333333334 + 4.333333334 + x = -2.962731473 + 4.333333334

Combine like terms: -4.333333334 + 4.333333334 = 0.000000000
0.000000000 + x = -2.962731473 + 4.333333334
x = -2.962731473 + 4.333333334

Combine like terms: -2.962731473 + 4.333333334 = 1.370601861
x = 1.370601861

Simplifying
x = 1.370601861


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.296064807, 1.370601861}
Solution
x = {7.296064807, 1.370601861}

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