3y^2-6y+2=0

Solution for 3y^2-6y+2=0 equation:

Simplifying
3y2 + -6y + 2 = 0

Reorder the terms:
2 + -6y + 3y2 = 0

Solving
2 + -6y + 3y2 = 0

Solving for variable 'y'.

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

Divide each side by '3'.
0.6666666667 + -2y + y2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -2y + -0.6666666667 + y2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -2y + y2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -2y + y2 = 0 + -0.6666666667
-2y + y2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-2y + y2 = -0.6666666667

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = -0.6666666667 + 1

Reorder the terms:
1 + -2y + y2 = -0.6666666667 + 1

Combine like terms: -0.6666666667 + 1 = 0.3333333333
1 + -2y + y2 = 0.3333333333

Factor a perfect square on the left side:
(y + -1)(y + -1) = 0.3333333333

Calculate the square root of the right side: 0.577350269

Break this problem into two subproblems by setting 
(y + -1) equal to 0.577350269 and -0.577350269.

Subproblem 1
y + -1 = 0.577350269

Simplifying
y + -1 = 0.577350269

Reorder the terms:
-1 + y = 0.577350269

Solving
-1 + y = 0.577350269

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = 0.577350269 + 1

Combine like terms: -1 + 1 = 0
0 + y = 0.577350269 + 1
y = 0.577350269 + 1

Combine like terms: 0.577350269 + 1 = 1.577350269
y = 1.577350269

Simplifying
y = 1.577350269

Subproblem 2
y + -1 = -0.577350269

Simplifying
y + -1 = -0.577350269

Reorder the terms:
-1 + y = -0.577350269

Solving
-1 + y = -0.577350269

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = -0.577350269 + 1

Combine like terms: -1 + 1 = 0
0 + y = -0.577350269 + 1
y = -0.577350269 + 1

Combine like terms: -0.577350269 + 1 = 0.422649731
y = 0.422649731

Simplifying
y = 0.422649731

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.577350269, 0.422649731}