-2r(6r^2-4r+1)=0

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Solution for -2r(6r^2-4r+1)=0 equation: 


Simplifying
-2r(6r2 + -4r + 1) = 0

Reorder the terms:
-2r(1 + -4r + 6r2) = 0
(1 * -2r + -4r * -2r + 6r2 * -2r) = 0
(-2r + 8r2 + -12r3) = 0

Solving
-2r + 8r2 + -12r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2r'.
2r(-1 + 4r + -6r2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0

Subproblem 2
Set the factor '(-1 + 4r + -6r2)' equal to zero and attempt to solve:

Simplifying
-1 + 4r + -6r2 = 0

Solving
-1 + 4r + -6r2 = 0

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

Divide each side by '-6'.
0.1666666667 + -0.6666666667r + r2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + -0.6666666667r + -0.1666666667 + r2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + -0.6666666667r + r2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + -0.6666666667r + r2 = 0 + -0.1666666667
-0.6666666667r + r2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
-0.6666666667r + r2 = -0.1666666667

The r term is -0.6666666667r.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667r + 0.1111111112 + r2 = -0.1666666667 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667r + r2 = -0.1666666667 + 0.1111111112

Combine like terms: -0.1666666667 + 0.1111111112 = -0.0555555555
0.1111111112 + -0.6666666667r + r2 = -0.0555555555

Factor a perfect square on the left side:
(r + -0.3333333334)(r + -0.3333333334) = -0.0555555555

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.
Solution
r = {0}

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