6y^2-6y-130=

Solution for 6y^2-6y-130= equation:

Simplifying
6y2 + -6y + -130 = 0

Reorder the terms:
-130 + -6y + 6y2 = 0

Solving
-130 + -6y + 6y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-65 + -3y + 3y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-65 + -3y + 3y2)' equal to zero and attempt to solve:

Simplifying
-65 + -3y + 3y2 = 0

Solving
-65 + -3y + 3y2 = 0

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

Divide each side by '3'.
-21.66666667 + -1y + y2 = 0

Move the constant term to the right:

Add '21.66666667' to each side of the equation.
-21.66666667 + -1y + 21.66666667 + y2 = 0 + 21.66666667

Reorder the terms:
-21.66666667 + 21.66666667 + -1y + y2 = 0 + 21.66666667

Combine like terms: -21.66666667 + 21.66666667 = 0.00000000
0.00000000 + -1y + y2 = 0 + 21.66666667
-1y + y2 = 0 + 21.66666667

Combine like terms: 0 + 21.66666667 = 21.66666667
-1y + y2 = 21.66666667

The y term is -1y.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1y + 0.25 + y2 = 21.66666667 + 0.25

Reorder the terms:
0.25 + -1y + y2 = 21.66666667 + 0.25

Combine like terms: 21.66666667 + 0.25 = 21.91666667
0.25 + -1y + y2 = 21.91666667

Factor a perfect square on the left side:
(y + -0.5)(y + -0.5) = 21.91666667

Calculate the square root of the right side: 4.681523969

Break this problem into two subproblems by setting 
(y + -0.5) equal to 4.681523969 and -4.681523969.

Subproblem 1
y + -0.5 = 4.681523969

Simplifying
y + -0.5 = 4.681523969

Reorder the terms:
-0.5 + y = 4.681523969

Solving
-0.5 + y = 4.681523969

Solving for variable 'y'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + y = 4.681523969 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = 4.681523969 + 0.5
y = 4.681523969 + 0.5

Combine like terms: 4.681523969 + 0.5 = 5.181523969
y = 5.181523969

Simplifying
y = 5.181523969

Subproblem 2
y + -0.5 = -4.681523969

Simplifying
y + -0.5 = -4.681523969

Reorder the terms:
-0.5 + y = -4.681523969

Solving
-0.5 + y = -4.681523969

Solving for variable 'y'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + y = -4.681523969 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = -4.681523969 + 0.5
y = -4.681523969 + 0.5

Combine like terms: -4.681523969 + 0.5 = -4.181523969
y = -4.181523969

Simplifying
y = -4.181523969

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.181523969, -4.181523969}
Solution
y = {5.181523969, -4.181523969}