(7y+7)(6y+6)=2

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

Simplifying
(7y + 7)(6y + 6) = 2

Reorder the terms:
(7 + 7y)(6y + 6) = 2

Reorder the terms:
(7 + 7y)(6 + 6y) = 2

Multiply (7 + 7y) * (6 + 6y)
(7(6 + 6y) + 7y * (6 + 6y)) = 2
((6 * 7 + 6y * 7) + 7y * (6 + 6y)) = 2
((42 + 42y) + 7y * (6 + 6y)) = 2
(42 + 42y + (6 * 7y + 6y * 7y)) = 2
(42 + 42y + (42y + 42y2)) = 2

Combine like terms: 42y + 42y = 84y
(42 + 84y + 42y2) = 2

Solving
42 + 84y + 42y2 = 2

Solving for variable 'y'.

Reorder the terms:
42 + -2 + 84y + 42y2 = 2 + -2

Combine like terms: 42 + -2 = 40
40 + 84y + 42y2 = 2 + -2

Combine like terms: 2 + -2 = 0
40 + 84y + 42y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + 42y + 21y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(20 + 42y + 21y2)' equal to zero and attempt to solve:

Simplifying
20 + 42y + 21y2 = 0

Solving
20 + 42y + 21y2 = 0

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

Divide each side by '21'.
0.9523809524 + 2y + y2 = 0

Move the constant term to the right:

Add '-0.9523809524' to each side of the equation.
0.9523809524 + 2y + -0.9523809524 + y2 = 0 + -0.9523809524

Reorder the terms:
0.9523809524 + -0.9523809524 + 2y + y2 = 0 + -0.9523809524

Combine like terms: 0.9523809524 + -0.9523809524 = 0.0000000000
0.0000000000 + 2y + y2 = 0 + -0.9523809524
2y + y2 = 0 + -0.9523809524

Combine like terms: 0 + -0.9523809524 = -0.9523809524
2y + y2 = -0.9523809524

The y term is 2y.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2y + 1 + y2 = -0.9523809524 + 1

Reorder the terms:
1 + 2y + y2 = -0.9523809524 + 1

Combine like terms: -0.9523809524 + 1 = 0.0476190476
1 + 2y + y2 = 0.0476190476

Factor a perfect square on the left side:
(y + 1)(y + 1) = 0.0476190476

Calculate the square root of the right side: 0.21821789

Break this problem into two subproblems by setting 
(y + 1) equal to 0.21821789 and -0.21821789.

Subproblem 1
y + 1 = 0.21821789

Simplifying
y + 1 = 0.21821789

Reorder the terms:
1 + y = 0.21821789

Solving
1 + y = 0.21821789

Solving for variable 'y'.

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

Add '-1' to each side of the equation.
1 + -1 + y = 0.21821789 + -1

Combine like terms: 1 + -1 = 0
0 + y = 0.21821789 + -1
y = 0.21821789 + -1

Combine like terms: 0.21821789 + -1 = -0.78178211
y = -0.78178211

Simplifying
y = -0.78178211

Subproblem 2
y + 1 = -0.21821789

Simplifying
y + 1 = -0.21821789

Reorder the terms:
1 + y = -0.21821789

Solving
1 + y = -0.21821789

Solving for variable 'y'.

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

Add '-1' to each side of the equation.
1 + -1 + y = -0.21821789 + -1

Combine like terms: 1 + -1 = 0
0 + y = -0.21821789 + -1
y = -0.21821789 + -1

Combine like terms: -0.21821789 + -1 = -1.21821789
y = -1.21821789

Simplifying
y = -1.21821789

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.78178211, -1.21821789}
Solution
y = {-0.78178211, -1.21821789}