9y^2-234y+189=0

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Solution for 9y^2-234y+189=0 equation: 


Simplifying
9y2 + -234y + 189 = 0

Reorder the terms:
189 + -234y + 9y2 = 0

Solving
189 + -234y + 9y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '9'.
9(21 + -26y + y2) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(21 + -26y + y2)' equal to zero and attempt to solve:

Simplifying
21 + -26y + y2 = 0

Solving
21 + -26y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + -26y + -21 + y2 = 0 + -21

Reorder the terms:
21 + -21 + -26y + y2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -26y + y2 = 0 + -21
-26y + y2 = 0 + -21

Combine like terms: 0 + -21 = -21
-26y + y2 = -21

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 = -21 + 169

Reorder the terms:
169 + -26y + y2 = -21 + 169

Combine like terms: -21 + 169 = 148
169 + -26y + y2 = 148

Factor a perfect square on the left side:
(y + -13)(y + -13) = 148

Calculate the square root of the right side: 12.165525061

Break this problem into two subproblems by setting 
(y + -13) equal to 12.165525061 and -12.165525061.


Subproblem 1
y + -13 = 12.165525061

Simplifying
y + -13 = 12.165525061

Reorder the terms:
-13 + y = 12.165525061

Solving
-13 + y = 12.165525061

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 = 12.165525061 + 13

Combine like terms: -13 + 13 = 0
0 + y = 12.165525061 + 13
y = 12.165525061 + 13

Combine like terms: 12.165525061 + 13 = 25.165525061
y = 25.165525061

Simplifying
y = 25.165525061


Subproblem 2
y + -13 = -12.165525061

Simplifying
y + -13 = -12.165525061

Reorder the terms:
-13 + y = -12.165525061

Solving
-13 + y = -12.165525061

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 = -12.165525061 + 13

Combine like terms: -13 + 13 = 0
0 + y = -12.165525061 + 13
y = -12.165525061 + 13

Combine like terms: -12.165525061 + 13 = 0.834474939
y = 0.834474939

Simplifying
y = 0.834474939


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {25.165525061, 0.834474939}
Solution
y = {25.165525061, 0.834474939}

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