12x^2-72x+80=0

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Solution for 12x^2-72x+80=0 equation: 


Simplifying
12x2 + -72x + 80 = 0

Reorder the terms:
80 + -72x + 12x2 = 0

Solving
80 + -72x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(20 + -18x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(20 + -18x + 3x2)' equal to zero and attempt to solve:

Simplifying
20 + -18x + 3x2 = 0

Solving
20 + -18x + 3x2 = 0

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

Divide each side by '3'.
6.666666667 + -6x + x2 = 0

Move the constant term to the right:

Add '-6.666666667' to each side of the equation.
6.666666667 + -6x + -6.666666667 + x2 = 0 + -6.666666667

Reorder the terms:
6.666666667 + -6.666666667 + -6x + x2 = 0 + -6.666666667

Combine like terms: 6.666666667 + -6.666666667 = 0.000000000
0.000000000 + -6x + x2 = 0 + -6.666666667
-6x + x2 = 0 + -6.666666667

Combine like terms: 0 + -6.666666667 = -6.666666667
-6x + x2 = -6.666666667

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -6.666666667 + 9

Reorder the terms:
9 + -6x + x2 = -6.666666667 + 9

Combine like terms: -6.666666667 + 9 = 2.333333333
9 + -6x + x2 = 2.333333333

Factor a perfect square on the left side:
(x + -3)(x + -3) = 2.333333333

Calculate the square root of the right side: 1.527525232

Break this problem into two subproblems by setting 
(x + -3) equal to 1.527525232 and -1.527525232.


Subproblem 1
x + -3 = 1.527525232

Simplifying
x + -3 = 1.527525232

Reorder the terms:
-3 + x = 1.527525232

Solving
-3 + x = 1.527525232

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 1.527525232 + 3

Combine like terms: -3 + 3 = 0
0 + x = 1.527525232 + 3
x = 1.527525232 + 3

Combine like terms: 1.527525232 + 3 = 4.527525232
x = 4.527525232

Simplifying
x = 4.527525232


Subproblem 2
x + -3 = -1.527525232

Simplifying
x + -3 = -1.527525232

Reorder the terms:
-3 + x = -1.527525232

Solving
-3 + x = -1.527525232

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -1.527525232 + 3

Combine like terms: -3 + 3 = 0
0 + x = -1.527525232 + 3
x = -1.527525232 + 3

Combine like terms: -1.527525232 + 3 = 1.472474768
x = 1.472474768

Simplifying
x = 1.472474768


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.527525232, 1.472474768}
Solution
x = {4.527525232, 1.472474768}

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