12x^2-104x+96=0

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Solution for 12x^2-104x+96=0 equation: 


Simplifying
12x2 + -104x + 96 = 0

Reorder the terms:
96 + -104x + 12x2 = 0

Solving
96 + -104x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(24 + -26x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(24 + -26x + 3x2)' equal to zero and attempt to solve:

Simplifying
24 + -26x + 3x2 = 0

Solving
24 + -26x + 3x2 = 0

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

Divide each side by '3'.
8 + -8.666666667x + x2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -8.666666667x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -8.666666667x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -8.666666667x + x2 = 0 + -8
-8.666666667x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-8.666666667x + x2 = -8

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 = -8 + 18.77777778

Reorder the terms:
18.77777778 + -8.666666667x + x2 = -8 + 18.77777778

Combine like terms: -8 + 18.77777778 = 10.77777778
18.77777778 + -8.666666667x + x2 = 10.77777778

Factor a perfect square on the left side:
(x + -4.333333334)(x + -4.333333334) = 10.77777778

Calculate the square root of the right side: 3.282952601

Break this problem into two subproblems by setting 
(x + -4.333333334) equal to 3.282952601 and -3.282952601.


Subproblem 1
x + -4.333333334 = 3.282952601

Simplifying
x + -4.333333334 = 3.282952601

Reorder the terms:
-4.333333334 + x = 3.282952601

Solving
-4.333333334 + x = 3.282952601

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 = 3.282952601 + 4.333333334

Combine like terms: -4.333333334 + 4.333333334 = 0.000000000
0.000000000 + x = 3.282952601 + 4.333333334
x = 3.282952601 + 4.333333334

Combine like terms: 3.282952601 + 4.333333334 = 7.616285935
x = 7.616285935

Simplifying
x = 7.616285935


Subproblem 2
x + -4.333333334 = -3.282952601

Simplifying
x + -4.333333334 = -3.282952601

Reorder the terms:
-4.333333334 + x = -3.282952601

Solving
-4.333333334 + x = -3.282952601

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 = -3.282952601 + 4.333333334

Combine like terms: -4.333333334 + 4.333333334 = 0.000000000
0.000000000 + x = -3.282952601 + 4.333333334
x = -3.282952601 + 4.333333334

Combine like terms: -3.282952601 + 4.333333334 = 1.050380733
x = 1.050380733

Simplifying
x = 1.050380733


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.616285935, 1.050380733}
Solution
x = {7.616285935, 1.050380733}

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