(y^2+6y-5)+(y+6)+(6y^2-y-5)=0

Solution for (y^2+6y-5)+(y+6)+(6y^2-y-5)=0 equation:

Simplifying
(y2 + 6y + -5) + (y + 6) + (6y2 + -1y + -5) = 0

Reorder the terms:
(-5 + 6y + y2) + (y + 6) + (6y2 + -1y + -5) = 0

Remove parenthesis around (-5 + 6y + y2)
-5 + 6y + y2 + (y + 6) + (6y2 + -1y + -5) = 0

Reorder the terms:
-5 + 6y + y2 + (6 + y) + (6y2 + -1y + -5) = 0

Remove parenthesis around (6 + y)
-5 + 6y + y2 + 6 + y + (6y2 + -1y + -5) = 0

Reorder the terms:
-5 + 6y + y2 + 6 + y + (-5 + -1y + 6y2) = 0

Remove parenthesis around (-5 + -1y + 6y2)
-5 + 6y + y2 + 6 + y + -5 + -1y + 6y2 = 0

Reorder the terms:
-5 + 6 + -5 + 6y + y + -1y + y2 + 6y2 = 0

Combine like terms: -5 + 6 = 1
1 + -5 + 6y + y + -1y + y2 + 6y2 = 0

Combine like terms: 1 + -5 = -4
-4 + 6y + y + -1y + y2 + 6y2 = 0

Combine like terms: 6y + y = 7y
-4 + 7y + -1y + y2 + 6y2 = 0

Combine like terms: 7y + -1y = 6y
-4 + 6y + y2 + 6y2 = 0

Combine like terms: y2 + 6y2 = 7y2
-4 + 6y + 7y2 = 0

Solving
-4 + 6y + 7y2 = 0

Solving for variable 'y'.

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

Divide each side by '7'.
-0.5714285714 + 0.8571428571y + y2 = 0

Move the constant term to the right:

Add '0.5714285714' to each side of the equation.
-0.5714285714 + 0.8571428571y + 0.5714285714 + y2 = 0 + 0.5714285714

Reorder the terms:
-0.5714285714 + 0.5714285714 + 0.8571428571y + y2 = 0 + 0.5714285714

Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000
0.0000000000 + 0.8571428571y + y2 = 0 + 0.5714285714
0.8571428571y + y2 = 0 + 0.5714285714

Combine like terms: 0 + 0.5714285714 = 0.5714285714
0.8571428571y + y2 = 0.5714285714

The y term is 0.8571428571y.  Take half its coefficient (0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
0.8571428571y + 0.1836734694 + y2 = 0.5714285714 + 0.1836734694

Reorder the terms:
0.1836734694 + 0.8571428571y + y2 = 0.5714285714 + 0.1836734694

Combine like terms: 0.5714285714 + 0.1836734694 = 0.7551020408
0.1836734694 + 0.8571428571y + y2 = 0.7551020408

Factor a perfect square on the left side:
(y + 0.4285714286)(y + 0.4285714286) = 0.7551020408

Calculate the square root of the right side: 0.868966076

Break this problem into two subproblems by setting 
(y + 0.4285714286) equal to 0.868966076 and -0.868966076.

Subproblem 1
y + 0.4285714286 = 0.868966076

Simplifying
y + 0.4285714286 = 0.868966076

Reorder the terms:
0.4285714286 + y = 0.868966076

Solving
0.4285714286 + y = 0.868966076

Solving for variable 'y'.

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

Add '-0.4285714286' to each side of the equation.
0.4285714286 + -0.4285714286 + y = 0.868966076 + -0.4285714286

Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000
0.0000000000 + y = 0.868966076 + -0.4285714286
y = 0.868966076 + -0.4285714286

Combine like terms: 0.868966076 + -0.4285714286 = 0.4403946474
y = 0.4403946474

Simplifying
y = 0.4403946474

Subproblem 2
y + 0.4285714286 = -0.868966076

Simplifying
y + 0.4285714286 = -0.868966076

Reorder the terms:
0.4285714286 + y = -0.868966076

Solving
0.4285714286 + y = -0.868966076

Solving for variable 'y'.

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

Add '-0.4285714286' to each side of the equation.
0.4285714286 + -0.4285714286 + y = -0.868966076 + -0.4285714286

Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000
0.0000000000 + y = -0.868966076 + -0.4285714286
y = -0.868966076 + -0.4285714286

Combine like terms: -0.868966076 + -0.4285714286 = -1.2975375046
y = -1.2975375046

Simplifying
y = -1.2975375046

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.4403946474, -1.2975375046}