6y^2-4y+2=0

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Solution for 6y^2-4y+2=0 equation: 


Simplifying
6y2 + -4y + 2 = 0

Reorder the terms:
2 + -4y + 6y2 = 0

Solving
2 + -4y + 6y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -2y + 3y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -2y + 3y2)' equal to zero and attempt to solve:

Simplifying
1 + -2y + 3y2 = 0

Solving
1 + -2y + 3y2 = 0

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

Divide each side by '3'.
0.3333333333 + -0.6666666667y + y2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -0.6666666667y + -0.3333333333 + y2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -0.6666666667y + y2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -0.6666666667y + y2 = 0 + -0.3333333333
-0.6666666667y + y2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-0.6666666667y + y2 = -0.3333333333

The y term is -0.6666666667y.  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.
-0.6666666667y + 0.1111111112 + y2 = -0.3333333333 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667y + y2 = -0.3333333333 + 0.1111111112

Combine like terms: -0.3333333333 + 0.1111111112 = -0.2222222221
0.1111111112 + -0.6666666667y + y2 = -0.2222222221

Factor a perfect square on the left side:
(y + -0.3333333334)(y + -0.3333333334) = -0.2222222221

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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