12x^2-104x+144=0

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Solution for 12x^2-104x+144=0 equation: 


Simplifying
12x2 + -104x + 144 = 0

Reorder the terms:
144 + -104x + 12x2 = 0

Solving
144 + -104x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(36 + -26x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(36 + -26x + 3x2)' equal to zero and attempt to solve:

Simplifying
36 + -26x + 3x2 = 0

Solving
36 + -26x + 3x2 = 0

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

Divide each side by '3'.
12 + -8.666666667x + x2 = 0

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -8.666666667x + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + -8.666666667x + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -8.666666667x + x2 = 0 + -12
-8.666666667x + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
-8.666666667x + x2 = -12

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 = -12 + 18.77777778

Reorder the terms:
18.77777778 + -8.666666667x + x2 = -12 + 18.77777778

Combine like terms: -12 + 18.77777778 = 6.77777778
18.77777778 + -8.666666667x + x2 = 6.77777778

Factor a perfect square on the left side:
(x + -4.333333334)(x + -4.333333334) = 6.77777778

Calculate the square root of the right side: 2.603416559

Break this problem into two subproblems by setting 
(x + -4.333333334) equal to 2.603416559 and -2.603416559.


Subproblem 1
x + -4.333333334 = 2.603416559

Simplifying
x + -4.333333334 = 2.603416559

Reorder the terms:
-4.333333334 + x = 2.603416559

Solving
-4.333333334 + x = 2.603416559

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 = 2.603416559 + 4.333333334

Combine like terms: -4.333333334 + 4.333333334 = 0.000000000
0.000000000 + x = 2.603416559 + 4.333333334
x = 2.603416559 + 4.333333334

Combine like terms: 2.603416559 + 4.333333334 = 6.936749893
x = 6.936749893

Simplifying
x = 6.936749893


Subproblem 2
x + -4.333333334 = -2.603416559

Simplifying
x + -4.333333334 = -2.603416559

Reorder the terms:
-4.333333334 + x = -2.603416559

Solving
-4.333333334 + x = -2.603416559

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 = -2.603416559 + 4.333333334

Combine like terms: -4.333333334 + 4.333333334 = 0.000000000
0.000000000 + x = -2.603416559 + 4.333333334
x = -2.603416559 + 4.333333334

Combine like terms: -2.603416559 + 4.333333334 = 1.729916775
x = 1.729916775

Simplifying
x = 1.729916775


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.936749893, 1.729916775}
Solution
x = {6.936749893, 1.729916775}

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