9y^2-234y+285=0

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Solution for 9y^2-234y+285=0 equation: 


Simplifying
9y2 + -234y + 285 = 0

Reorder the terms:
285 + -234y + 9y2 = 0

Solving
285 + -234y + 9y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(95 + -78y + 3y2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(95 + -78y + 3y2)' equal to zero and attempt to solve:

Simplifying
95 + -78y + 3y2 = 0

Solving
95 + -78y + 3y2 = 0

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

Divide each side by '3'.
31.66666667 + -26y + y2 = 0

Move the constant term to the right:

Add '-31.66666667' to each side of the equation.
31.66666667 + -26y + -31.66666667 + y2 = 0 + -31.66666667

Reorder the terms:
31.66666667 + -31.66666667 + -26y + y2 = 0 + -31.66666667

Combine like terms: 31.66666667 + -31.66666667 = 0.00000000
0.00000000 + -26y + y2 = 0 + -31.66666667
-26y + y2 = 0 + -31.66666667

Combine like terms: 0 + -31.66666667 = -31.66666667
-26y + y2 = -31.66666667

The y term is -26y.  Take half its coefficient (-13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
-26y + 169 + y2 = -31.66666667 + 169

Reorder the terms:
169 + -26y + y2 = -31.66666667 + 169

Combine like terms: -31.66666667 + 169 = 137.33333333
169 + -26y + y2 = 137.33333333

Factor a perfect square on the left side:
(y + -13)(y + -13) = 137.33333333

Calculate the square root of the right side: 11.718930554

Break this problem into two subproblems by setting 
(y + -13) equal to 11.718930554 and -11.718930554.


Subproblem 1
y + -13 = 11.718930554

Simplifying
y + -13 = 11.718930554

Reorder the terms:
-13 + y = 11.718930554

Solving
-13 + y = 11.718930554

Solving for variable 'y'.

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

Add '13' to each side of the equation.
-13 + 13 + y = 11.718930554 + 13

Combine like terms: -13 + 13 = 0
0 + y = 11.718930554 + 13
y = 11.718930554 + 13

Combine like terms: 11.718930554 + 13 = 24.718930554
y = 24.718930554

Simplifying
y = 24.718930554


Subproblem 2
y + -13 = -11.718930554

Simplifying
y + -13 = -11.718930554

Reorder the terms:
-13 + y = -11.718930554

Solving
-13 + y = -11.718930554

Solving for variable 'y'.

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

Add '13' to each side of the equation.
-13 + 13 + y = -11.718930554 + 13

Combine like terms: -13 + 13 = 0
0 + y = -11.718930554 + 13
y = -11.718930554 + 13

Combine like terms: -11.718930554 + 13 = 1.281069446
y = 1.281069446

Simplifying
y = 1.281069446


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {24.718930554, 1.281069446}
Solution
y = {24.718930554, 1.281069446}

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