-3y^2+54y-36=0

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Solution for -3y^2+54y-36=0 equation: 


Simplifying
-3y2 + 54y + -36 = 0

Reorder the terms:
-36 + 54y + -3y2 = 0

Solving
-36 + 54y + -3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + 18y + -1y2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-12 + 18y + -1y2)' equal to zero and attempt to solve:

Simplifying
-12 + 18y + -1y2 = 0

Solving
-12 + 18y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
12 + -18y + y2 = 0

Move the constant term to the right:

Add '-12' to each side of the equation.
12 + -18y + -12 + y2 = 0 + -12

Reorder the terms:
12 + -12 + -18y + y2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -18y + y2 = 0 + -12
-18y + y2 = 0 + -12

Combine like terms: 0 + -12 = -12
-18y + y2 = -12

The y term is -18y.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18y + 81 + y2 = -12 + 81

Reorder the terms:
81 + -18y + y2 = -12 + 81

Combine like terms: -12 + 81 = 69
81 + -18y + y2 = 69

Factor a perfect square on the left side:
(y + -9)(y + -9) = 69

Calculate the square root of the right side: 8.306623863

Break this problem into two subproblems by setting 
(y + -9) equal to 8.306623863 and -8.306623863.


Subproblem 1
y + -9 = 8.306623863

Simplifying
y + -9 = 8.306623863

Reorder the terms:
-9 + y = 8.306623863

Solving
-9 + y = 8.306623863

Solving for variable 'y'.

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

Add '9' to each side of the equation.
-9 + 9 + y = 8.306623863 + 9

Combine like terms: -9 + 9 = 0
0 + y = 8.306623863 + 9
y = 8.306623863 + 9

Combine like terms: 8.306623863 + 9 = 17.306623863
y = 17.306623863

Simplifying
y = 17.306623863


Subproblem 2
y + -9 = -8.306623863

Simplifying
y + -9 = -8.306623863

Reorder the terms:
-9 + y = -8.306623863

Solving
-9 + y = -8.306623863

Solving for variable 'y'.

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

Add '9' to each side of the equation.
-9 + 9 + y = -8.306623863 + 9

Combine like terms: -9 + 9 = 0
0 + y = -8.306623863 + 9
y = -8.306623863 + 9

Combine like terms: -8.306623863 + 9 = 0.693376137
y = 0.693376137

Simplifying
y = 0.693376137


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {17.306623863, 0.693376137}
Solution
y = {17.306623863, 0.693376137}

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