6y^2-2y+6=0

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

Simplifying
6y2 + -2y + 6 = 0

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

Solving
6 + -2y + 6y2 = 0

Solving for variable 'y'.

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

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

Simplifying
3 + -1y + 3y2 = 0

Solving
3 + -1y + 3y2 = 0

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

Divide each side by '3'.
1 + -0.3333333333y + y2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -0.3333333333y + -1 + y2 = 0 + -1

Reorder the terms:
1 + -1 + -0.3333333333y + y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -0.3333333333y + y2 = 0 + -1
-0.3333333333y + y2 = 0 + -1

Combine like terms: 0 + -1 = -1
-0.3333333333y + y2 = -1

The y term is -0.3333333333y.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333y + 0.02777777779 + y2 = -1 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333y + y2 = -1 + 0.02777777779

Combine like terms: -1 + 0.02777777779 = -0.97222222221
0.02777777779 + -0.3333333333y + y2 = -0.97222222221

Factor a perfect square on the left side:
(y + -0.1666666667)(y + -0.1666666667) = -0.97222222221

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.