12x^2-52x+80=0

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Solution for 12x^2-52x+80=0 equation: 


Simplifying
12x2 + -52x + 80 = 0

Reorder the terms:
80 + -52x + 12x2 = 0

Solving
80 + -52x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(20 + -13x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(20 + -13x + 3x2)' equal to zero and attempt to solve:

Simplifying
20 + -13x + 3x2 = 0

Solving
20 + -13x + 3x2 = 0

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

Divide each side by '3'.
6.666666667 + -4.333333333x + x2 = 0

Move the constant term to the right:

Add '-6.666666667' to each side of the equation.
6.666666667 + -4.333333333x + -6.666666667 + x2 = 0 + -6.666666667

Reorder the terms:
6.666666667 + -6.666666667 + -4.333333333x + x2 = 0 + -6.666666667

Combine like terms: 6.666666667 + -6.666666667 = 0.000000000
0.000000000 + -4.333333333x + x2 = 0 + -6.666666667
-4.333333333x + x2 = 0 + -6.666666667

Combine like terms: 0 + -6.666666667 = -6.666666667
-4.333333333x + x2 = -6.666666667

The x term is -4.333333333x.  Take half its coefficient (-2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
-4.333333333x + 4.694444446 + x2 = -6.666666667 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333x + x2 = -6.666666667 + 4.694444446

Combine like terms: -6.666666667 + 4.694444446 = -1.972222221
4.694444446 + -4.333333333x + x2 = -1.972222221

Factor a perfect square on the left side:
(x + -2.166666667)(x + -2.166666667) = -1.972222221

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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