9y^2-396y+2628=0

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Solution for 9y^2-396y+2628=0 equation: 


Simplifying
9y2 + -396y + 2628 = 0

Reorder the terms:
2628 + -396y + 9y2 = 0

Solving
2628 + -396y + 9y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '9'.
9(292 + -44y + y2) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(292 + -44y + y2)' equal to zero and attempt to solve:

Simplifying
292 + -44y + y2 = 0

Solving
292 + -44y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-292' to each side of the equation.
292 + -44y + -292 + y2 = 0 + -292

Reorder the terms:
292 + -292 + -44y + y2 = 0 + -292

Combine like terms: 292 + -292 = 0
0 + -44y + y2 = 0 + -292
-44y + y2 = 0 + -292

Combine like terms: 0 + -292 = -292
-44y + y2 = -292

The y term is -44y.  Take half its coefficient (-22).
Square it (484) and add it to both sides.

Add '484' to each side of the equation.
-44y + 484 + y2 = -292 + 484

Reorder the terms:
484 + -44y + y2 = -292 + 484

Combine like terms: -292 + 484 = 192
484 + -44y + y2 = 192

Factor a perfect square on the left side:
(y + -22)(y + -22) = 192

Calculate the square root of the right side: 13.856406461

Break this problem into two subproblems by setting 
(y + -22) equal to 13.856406461 and -13.856406461.


Subproblem 1
y + -22 = 13.856406461

Simplifying
y + -22 = 13.856406461

Reorder the terms:
-22 + y = 13.856406461

Solving
-22 + y = 13.856406461

Solving for variable 'y'.

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

Add '22' to each side of the equation.
-22 + 22 + y = 13.856406461 + 22

Combine like terms: -22 + 22 = 0
0 + y = 13.856406461 + 22
y = 13.856406461 + 22

Combine like terms: 13.856406461 + 22 = 35.856406461
y = 35.856406461

Simplifying
y = 35.856406461


Subproblem 2
y + -22 = -13.856406461

Simplifying
y + -22 = -13.856406461

Reorder the terms:
-22 + y = -13.856406461

Solving
-22 + y = -13.856406461

Solving for variable 'y'.

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

Add '22' to each side of the equation.
-22 + 22 + y = -13.856406461 + 22

Combine like terms: -22 + 22 = 0
0 + y = -13.856406461 + 22
y = -13.856406461 + 22

Combine like terms: -13.856406461 + 22 = 8.143593539
y = 8.143593539

Simplifying
y = 8.143593539


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {35.856406461, 8.143593539}
Solution
y = {35.856406461, 8.143593539}

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