3y^2-36y+9=0

Solution for 3y^2-36y+9=0 equation:

Simplifying
3y2 + -36y + 9 = 0

Reorder the terms:
9 + -36y + 3y2 = 0

Solving
9 + -36y + 3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -12y + y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + -12y + y2)' equal to zero and attempt to solve:

Simplifying
3 + -12y + y2 = 0

Solving
3 + -12y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -12y + -3 + y2 = 0 + -3

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

Combine like terms: 3 + -3 = 0
0 + -12y + y2 = 0 + -3
-12y + y2 = 0 + -3

Combine like terms: 0 + -3 = -3
-12y + y2 = -3

The y term is -12y.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12y + 36 + y2 = -3 + 36

Reorder the terms:
36 + -12y + y2 = -3 + 36

Combine like terms: -3 + 36 = 33
36 + -12y + y2 = 33

Factor a perfect square on the left side:
(y + -6)(y + -6) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(y + -6) equal to 5.744562647 and -5.744562647.

Subproblem 1
y + -6 = 5.744562647

Simplifying
y + -6 = 5.744562647

Reorder the terms:
-6 + y = 5.744562647

Solving
-6 + y = 5.744562647

Solving for variable 'y'.

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

Add '6' to each side of the equation.
-6 + 6 + y = 5.744562647 + 6

Combine like terms: -6 + 6 = 0
0 + y = 5.744562647 + 6
y = 5.744562647 + 6

Combine like terms: 5.744562647 + 6 = 11.744562647
y = 11.744562647

Simplifying
y = 11.744562647

Subproblem 2
y + -6 = -5.744562647

Simplifying
y + -6 = -5.744562647

Reorder the terms:
-6 + y = -5.744562647

Solving
-6 + y = -5.744562647

Solving for variable 'y'.

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

Add '6' to each side of the equation.
-6 + 6 + y = -5.744562647 + 6

Combine like terms: -6 + 6 = 0
0 + y = -5.744562647 + 6
y = -5.744562647 + 6

Combine like terms: -5.744562647 + 6 = 0.255437353
y = 0.255437353

Simplifying
y = 0.255437353

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {11.744562647, 0.255437353}
Solution
y = {11.744562647, 0.255437353}