12x^2-88x+72=0

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Solution for 12x^2-88x+72=0 equation: 


Simplifying
12x2 + -88x + 72 = 0

Reorder the terms:
72 + -88x + 12x2 = 0

Solving
72 + -88x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(18 + -22x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(18 + -22x + 3x2)' equal to zero and attempt to solve:

Simplifying
18 + -22x + 3x2 = 0

Solving
18 + -22x + 3x2 = 0

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

Divide each side by '3'.
6 + -7.333333333x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -7.333333333x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -7.333333333x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7.333333333x + x2 = 0 + -6
-7.333333333x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-7.333333333x + x2 = -6

The x term is -7.333333333x.  Take half its coefficient (-3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
-7.333333333x + 13.44444445 + x2 = -6 + 13.44444445

Reorder the terms:
13.44444445 + -7.333333333x + x2 = -6 + 13.44444445

Combine like terms: -6 + 13.44444445 = 7.44444445
13.44444445 + -7.333333333x + x2 = 7.44444445

Factor a perfect square on the left side:
(x + -3.666666667)(x + -3.666666667) = 7.44444445

Calculate the square root of the right side: 2.728450925

Break this problem into two subproblems by setting 
(x + -3.666666667) equal to 2.728450925 and -2.728450925.


Subproblem 1
x + -3.666666667 = 2.728450925

Simplifying
x + -3.666666667 = 2.728450925

Reorder the terms:
-3.666666667 + x = 2.728450925

Solving
-3.666666667 + x = 2.728450925

Solving for variable 'x'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + x = 2.728450925 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + x = 2.728450925 + 3.666666667
x = 2.728450925 + 3.666666667

Combine like terms: 2.728450925 + 3.666666667 = 6.395117592
x = 6.395117592

Simplifying
x = 6.395117592


Subproblem 2
x + -3.666666667 = -2.728450925

Simplifying
x + -3.666666667 = -2.728450925

Reorder the terms:
-3.666666667 + x = -2.728450925

Solving
-3.666666667 + x = -2.728450925

Solving for variable 'x'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + x = -2.728450925 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + x = -2.728450925 + 3.666666667
x = -2.728450925 + 3.666666667

Combine like terms: -2.728450925 + 3.666666667 = 0.938215742
x = 0.938215742

Simplifying
x = 0.938215742


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.395117592, 0.938215742}
Solution
x = {6.395117592, 0.938215742}

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