3y^2-36y-63=0

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Solution for 3y^2-36y-63=0 equation: 


Simplifying
3y2 + -36y + -63 = 0

Reorder the terms:
-63 + -36y + 3y2 = 0

Solving
-63 + -36y + 3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-21 + -12y + y2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-21 + -12y + y2)' equal to zero and attempt to solve:

Simplifying
-21 + -12y + y2 = 0

Solving
-21 + -12y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + -12y + 21 + y2 = 0 + 21

Reorder the terms:
-21 + 21 + -12y + y2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -12y + y2 = 0 + 21
-12y + y2 = 0 + 21

Combine like terms: 0 + 21 = 21
-12y + y2 = 21

The y term is -12y.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12y + 36 + y2 = 21 + 36

Reorder the terms:
36 + -12y + y2 = 21 + 36

Combine like terms: 21 + 36 = 57
36 + -12y + y2 = 57

Factor a perfect square on the left side:
(y + -6)(y + -6) = 57

Calculate the square root of the right side: 7.549834435

Break this problem into two subproblems by setting 
(y + -6) equal to 7.549834435 and -7.549834435.


Subproblem 1
y + -6 = 7.549834435

Simplifying
y + -6 = 7.549834435

Reorder the terms:
-6 + y = 7.549834435

Solving
-6 + y = 7.549834435

Solving for variable 'y'.

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

Add '6' to each side of the equation.
-6 + 6 + y = 7.549834435 + 6

Combine like terms: -6 + 6 = 0
0 + y = 7.549834435 + 6
y = 7.549834435 + 6

Combine like terms: 7.549834435 + 6 = 13.549834435
y = 13.549834435

Simplifying
y = 13.549834435


Subproblem 2
y + -6 = -7.549834435

Simplifying
y + -6 = -7.549834435

Reorder the terms:
-6 + y = -7.549834435

Solving
-6 + y = -7.549834435

Solving for variable 'y'.

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

Add '6' to each side of the equation.
-6 + 6 + y = -7.549834435 + 6

Combine like terms: -6 + 6 = 0
0 + y = -7.549834435 + 6
y = -7.549834435 + 6

Combine like terms: -7.549834435 + 6 = -1.549834435
y = -1.549834435

Simplifying
y = -1.549834435


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {13.549834435, -1.549834435}
Solution
y = {13.549834435, -1.549834435}

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