9y^2-60y+66=0

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Solution for 9y^2-60y+66=0 equation: 


Simplifying
9y2 + -60y + 66 = 0

Reorder the terms:
66 + -60y + 9y2 = 0

Solving
66 + -60y + 9y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(22 + -20y + 3y2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(22 + -20y + 3y2)' equal to zero and attempt to solve:

Simplifying
22 + -20y + 3y2 = 0

Solving
22 + -20y + 3y2 = 0

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

Divide each side by '3'.
7.333333333 + -6.666666667y + y2 = 0

Move the constant term to the right:

Add '-7.333333333' to each side of the equation.
7.333333333 + -6.666666667y + -7.333333333 + y2 = 0 + -7.333333333

Reorder the terms:
7.333333333 + -7.333333333 + -6.666666667y + y2 = 0 + -7.333333333

Combine like terms: 7.333333333 + -7.333333333 = 0.000000000
0.000000000 + -6.666666667y + y2 = 0 + -7.333333333
-6.666666667y + y2 = 0 + -7.333333333

Combine like terms: 0 + -7.333333333 = -7.333333333
-6.666666667y + y2 = -7.333333333

The y term is -6.666666667y.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667y + 11.11111112 + y2 = -7.333333333 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667y + y2 = -7.333333333 + 11.11111112

Combine like terms: -7.333333333 + 11.11111112 = 3.777777787
11.11111112 + -6.666666667y + y2 = 3.777777787

Factor a perfect square on the left side:
(y + -3.333333334)(y + -3.333333334) = 3.777777787

Calculate the square root of the right side: 1.943650634

Break this problem into two subproblems by setting 
(y + -3.333333334) equal to 1.943650634 and -1.943650634.


Subproblem 1
y + -3.333333334 = 1.943650634

Simplifying
y + -3.333333334 = 1.943650634

Reorder the terms:
-3.333333334 + y = 1.943650634

Solving
-3.333333334 + y = 1.943650634

Solving for variable 'y'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + y = 1.943650634 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + y = 1.943650634 + 3.333333334
y = 1.943650634 + 3.333333334

Combine like terms: 1.943650634 + 3.333333334 = 5.276983968
y = 5.276983968

Simplifying
y = 5.276983968


Subproblem 2
y + -3.333333334 = -1.943650634

Simplifying
y + -3.333333334 = -1.943650634

Reorder the terms:
-3.333333334 + y = -1.943650634

Solving
-3.333333334 + y = -1.943650634

Solving for variable 'y'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + y = -1.943650634 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + y = -1.943650634 + 3.333333334
y = -1.943650634 + 3.333333334

Combine like terms: -1.943650634 + 3.333333334 = 1.3896827
y = 1.3896827

Simplifying
y = 1.3896827


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.276983968, 1.3896827}
Solution
y = {5.276983968, 1.3896827}

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