12y^2-28y+12=0

Solution for 12y^2-28y+12=0 equation:

Simplifying
12y2 + -28y + 12 = 0

Reorder the terms:
12 + -28y + 12y2 = 0

Solving
12 + -28y + 12y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + -7y + 3y2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + -7y + 3y2)' equal to zero and attempt to solve:

Simplifying
3 + -7y + 3y2 = 0

Solving
3 + -7y + 3y2 = 0

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

Divide each side by '3'.
1 + -2.333333333y + y2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2.333333333y + -1 + y2 = 0 + -1

Reorder the terms:
1 + -1 + -2.333333333y + y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2.333333333y + y2 = 0 + -1
-2.333333333y + y2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2.333333333y + y2 = -1

The y term is -2.333333333y.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333y + 1.361111112 + y2 = -1 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333y + y2 = -1 + 1.361111112

Combine like terms: -1 + 1.361111112 = 0.361111112
1.361111112 + -2.333333333y + y2 = 0.361111112

Factor a perfect square on the left side:
(y + -1.166666667)(y + -1.166666667) = 0.361111112

Calculate the square root of the right side: 0.600925213

Break this problem into two subproblems by setting 
(y + -1.166666667) equal to 0.600925213 and -0.600925213.

Subproblem 1
y + -1.166666667 = 0.600925213

Simplifying
y + -1.166666667 = 0.600925213

Reorder the terms:
-1.166666667 + y = 0.600925213

Solving
-1.166666667 + y = 0.600925213

Solving for variable 'y'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + y = 0.600925213 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + y = 0.600925213 + 1.166666667
y = 0.600925213 + 1.166666667

Combine like terms: 0.600925213 + 1.166666667 = 1.76759188
y = 1.76759188

Simplifying
y = 1.76759188

Subproblem 2
y + -1.166666667 = -0.600925213

Simplifying
y + -1.166666667 = -0.600925213

Reorder the terms:
-1.166666667 + y = -0.600925213

Solving
-1.166666667 + y = -0.600925213

Solving for variable 'y'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + y = -0.600925213 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + y = -0.600925213 + 1.166666667
y = -0.600925213 + 1.166666667

Combine like terms: -0.600925213 + 1.166666667 = 0.565741454
y = 0.565741454

Simplifying
y = 0.565741454

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.76759188, 0.565741454}
Solution
y = {1.76759188, 0.565741454}