(-7y^2-7y)+(6y^2+y-1)=

Solution for (-7y^2-7y)+(6y^2+y-1)= equation:

Simplifying
(-7y2 + -7y) + (6y2 + y + -1) = 0

Reorder the terms:
(-7y + -7y2) + (6y2 + y + -1) = 0

Remove parenthesis around (-7y + -7y2)
-7y + -7y2 + (6y2 + y + -1) = 0

Reorder the terms:
-7y + -7y2 + (-1 + y + 6y2) = 0

Remove parenthesis around (-1 + y + 6y2)
-7y + -7y2 + -1 + y + 6y2 = 0

Reorder the terms:
-1 + -7y + y + -7y2 + 6y2 = 0

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

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

Solving
-1 + -6y + -1y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 6y + y2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(1 + 6y + y2)' equal to zero and attempt to solve:

Simplifying
1 + 6y + y2 = 0

Solving
1 + 6y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 6y + -1 + y2 = 0 + -1

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

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

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

The y term is 6y.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6y + 9 + y2 = -1 + 9

Reorder the terms:
9 + 6y + y2 = -1 + 9

Combine like terms: -1 + 9 = 8
9 + 6y + y2 = 8

Factor a perfect square on the left side:
(y + 3)(y + 3) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(y + 3) equal to 2.828427125 and -2.828427125.

Subproblem 1
y + 3 = 2.828427125

Simplifying
y + 3 = 2.828427125

Reorder the terms:
3 + y = 2.828427125

Solving
3 + y = 2.828427125

Solving for variable 'y'.

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

Add '-3' to each side of the equation.
3 + -3 + y = 2.828427125 + -3

Combine like terms: 3 + -3 = 0
0 + y = 2.828427125 + -3
y = 2.828427125 + -3

Combine like terms: 2.828427125 + -3 = -0.171572875
y = -0.171572875

Simplifying
y = -0.171572875

Subproblem 2
y + 3 = -2.828427125

Simplifying
y + 3 = -2.828427125

Reorder the terms:
3 + y = -2.828427125

Solving
3 + y = -2.828427125

Solving for variable 'y'.

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

Add '-3' to each side of the equation.
3 + -3 + y = -2.828427125 + -3

Combine like terms: 3 + -3 = 0
0 + y = -2.828427125 + -3
y = -2.828427125 + -3

Combine like terms: -2.828427125 + -3 = -5.828427125
y = -5.828427125

Simplifying
y = -5.828427125

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.171572875, -5.828427125}
Solution
y = {-0.171572875, -5.828427125}