12r^2-26r+20=0

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Solution for 12r^2-26r+20=0 equation: 


Simplifying
12r2 + -26r + 20 = 0

Reorder the terms:
20 + -26r + 12r2 = 0

Solving
20 + -26r + 12r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -13r + 6r2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(10 + -13r + 6r2)' equal to zero and attempt to solve:

Simplifying
10 + -13r + 6r2 = 0

Solving
10 + -13r + 6r2 = 0

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

Divide each side by '6'.
1.666666667 + -2.166666667r + r2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -2.166666667r + -1.666666667 + r2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -2.166666667r + r2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -2.166666667r + r2 = 0 + -1.666666667
-2.166666667r + r2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-2.166666667r + r2 = -1.666666667

The r term is -2.166666667r.  Take half its coefficient (-1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
-2.166666667r + 1.173611113 + r2 = -1.666666667 + 1.173611113

Reorder the terms:
1.173611113 + -2.166666667r + r2 = -1.666666667 + 1.173611113

Combine like terms: -1.666666667 + 1.173611113 = -0.493055554
1.173611113 + -2.166666667r + r2 = -0.493055554

Factor a perfect square on the left side:
(r + -1.083333334)(r + -1.083333334) = -0.493055554

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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