3y^2-12y+4=0

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Solution for 3y^2-12y+4=0 equation: 


Simplifying
3y2 + -12y + 4 = 0

Reorder the terms:
4 + -12y + 3y2 = 0

Solving
4 + -12y + 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'.
1.333333333 + -4y + y2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -4y + -1.333333333 + y2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -4y + y2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -4y + y2 = 0 + -1.333333333
-4y + y2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-4y + y2 = -1.333333333

The y term is -4y.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4y + 4 + y2 = -1.333333333 + 4

Reorder the terms:
4 + -4y + y2 = -1.333333333 + 4

Combine like terms: -1.333333333 + 4 = 2.666666667
4 + -4y + y2 = 2.666666667

Factor a perfect square on the left side:
(y + -2)(y + -2) = 2.666666667

Calculate the square root of the right side: 1.632993162

Break this problem into two subproblems by setting 
(y + -2) equal to 1.632993162 and -1.632993162.


Subproblem 1
y + -2 = 1.632993162

Simplifying
y + -2 = 1.632993162

Reorder the terms:
-2 + y = 1.632993162

Solving
-2 + y = 1.632993162

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = 1.632993162 + 2

Combine like terms: -2 + 2 = 0
0 + y = 1.632993162 + 2
y = 1.632993162 + 2

Combine like terms: 1.632993162 + 2 = 3.632993162
y = 3.632993162

Simplifying
y = 3.632993162


Subproblem 2
y + -2 = -1.632993162

Simplifying
y + -2 = -1.632993162

Reorder the terms:
-2 + y = -1.632993162

Solving
-2 + y = -1.632993162

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = -1.632993162 + 2

Combine like terms: -2 + 2 = 0
0 + y = -1.632993162 + 2
y = -1.632993162 + 2

Combine like terms: -1.632993162 + 2 = 0.367006838
y = 0.367006838

Simplifying
y = 0.367006838


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.632993162, 0.367006838}

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