-3y^2+84y+27=0

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Solution for -3y^2+84y+27=0 equation: 


Simplifying
-3y2 + 84y + 27 = 0

Reorder the terms:
27 + 84y + -3y2 = 0

Solving
27 + 84y + -3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + 28y + -1y2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(9 + 28y + -1y2)' equal to zero and attempt to solve:

Simplifying
9 + 28y + -1y2 = 0

Solving
9 + 28y + -1y2 = 0

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

Divide each side by '-1'.
-9 + -28y + y2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -28y + 9 + y2 = 0 + 9

Reorder the terms:
-9 + 9 + -28y + y2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -28y + y2 = 0 + 9
-28y + y2 = 0 + 9

Combine like terms: 0 + 9 = 9
-28y + y2 = 9

The y term is -28y.  Take half its coefficient (-14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
-28y + 196 + y2 = 9 + 196

Reorder the terms:
196 + -28y + y2 = 9 + 196

Combine like terms: 9 + 196 = 205
196 + -28y + y2 = 205

Factor a perfect square on the left side:
(y + -14)(y + -14) = 205

Calculate the square root of the right side: 14.317821063

Break this problem into two subproblems by setting 
(y + -14) equal to 14.317821063 and -14.317821063.


Subproblem 1
y + -14 = 14.317821063

Simplifying
y + -14 = 14.317821063

Reorder the terms:
-14 + y = 14.317821063

Solving
-14 + y = 14.317821063

Solving for variable 'y'.

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

Add '14' to each side of the equation.
-14 + 14 + y = 14.317821063 + 14

Combine like terms: -14 + 14 = 0
0 + y = 14.317821063 + 14
y = 14.317821063 + 14

Combine like terms: 14.317821063 + 14 = 28.317821063
y = 28.317821063

Simplifying
y = 28.317821063


Subproblem 2
y + -14 = -14.317821063

Simplifying
y + -14 = -14.317821063

Reorder the terms:
-14 + y = -14.317821063

Solving
-14 + y = -14.317821063

Solving for variable 'y'.

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

Add '14' to each side of the equation.
-14 + 14 + y = -14.317821063 + 14

Combine like terms: -14 + 14 = 0
0 + y = -14.317821063 + 14
y = -14.317821063 + 14

Combine like terms: -14.317821063 + 14 = -0.317821063
y = -0.317821063

Simplifying
y = -0.317821063


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {28.317821063, -0.317821063}
Solution
y = {28.317821063, -0.317821063}

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