(y+5)(y+7)=2

Solution for (y+5)(y+7)=2 equation:

Simplifying
(y + 5)(y + 7) = 2

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

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

Multiply (5 + y) * (7 + y)
(5(7 + y) + y(7 + y)) = 2
((7 * 5 + y * 5) + y(7 + y)) = 2
((35 + 5y) + y(7 + y)) = 2
(35 + 5y + (7 * y + y * y)) = 2
(35 + 5y + (7y + y2)) = 2

Combine like terms: 5y + 7y = 12y
(35 + 12y + y2) = 2

Solving
35 + 12y + y2 = 2

Solving for variable 'y'.

Reorder the terms:
35 + -2 + 12y + y2 = 2 + -2

Combine like terms: 35 + -2 = 33
33 + 12y + y2 = 2 + -2

Combine like terms: 2 + -2 = 0
33 + 12y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-33' to each side of the equation.
33 + 12y + -33 + y2 = 0 + -33

Reorder the terms:
33 + -33 + 12y + y2 = 0 + -33

Combine like terms: 33 + -33 = 0
0 + 12y + y2 = 0 + -33
12y + y2 = 0 + -33

Combine like terms: 0 + -33 = -33
12y + y2 = -33

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 = -33 + 36

Reorder the terms:
36 + 12y + y2 = -33 + 36

Combine like terms: -33 + 36 = 3
36 + 12y + y2 = 3

Factor a perfect square on the left side:
(y + 6)(y + 6) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(y + 6) equal to 1.732050808 and -1.732050808.

Subproblem 1
y + 6 = 1.732050808

Simplifying
y + 6 = 1.732050808

Reorder the terms:
6 + y = 1.732050808

Solving
6 + y = 1.732050808

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 = 1.732050808 + -6

Combine like terms: 6 + -6 = 0
0 + y = 1.732050808 + -6
y = 1.732050808 + -6

Combine like terms: 1.732050808 + -6 = -4.267949192
y = -4.267949192

Simplifying
y = -4.267949192

Subproblem 2
y + 6 = -1.732050808

Simplifying
y + 6 = -1.732050808

Reorder the terms:
6 + y = -1.732050808

Solving
6 + y = -1.732050808

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 = -1.732050808 + -6

Combine like terms: 6 + -6 = 0
0 + y = -1.732050808 + -6
y = -1.732050808 + -6

Combine like terms: -1.732050808 + -6 = -7.732050808
y = -7.732050808

Simplifying
y = -7.732050808

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-4.267949192, -7.732050808}