(y+6)(y+6)=1

Solution for (y+6)(y+6)=1 equation:

Simplifying
(y + 6)(y + 6) = 1

Reorder the terms:
(6 + y)(y + 6) = 1

Reorder the terms:
(6 + y)(6 + y) = 1

Multiply (6 + y) * (6 + y)
(6(6 + y) + y(6 + y)) = 1
((6 * 6 + y * 6) + y(6 + y)) = 1
((36 + 6y) + y(6 + y)) = 1
(36 + 6y + (6 * y + y * y)) = 1
(36 + 6y + (6y + y2)) = 1

Combine like terms: 6y + 6y = 12y
(36 + 12y + y2) = 1

Solving
36 + 12y + y2 = 1

Solving for variable 'y'.

Reorder the terms:
36 + -1 + 12y + y2 = 1 + -1

Combine like terms: 36 + -1 = 35
35 + 12y + y2 = 1 + -1

Combine like terms: 1 + -1 = 0
35 + 12y + y2 = 0

Factor a trinomial.
(7 + y)(5 + y) = 0

Subproblem 1
Set the factor '(7 + y)' equal to zero and attempt to solve:

Simplifying
7 + y = 0

Solving
7 + y = 0

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

Add '-7' to each side of the equation.
7 + -7 + y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + y = 0 + -7
y = 0 + -7

Combine like terms: 0 + -7 = -7
y = -7

Simplifying
y = -7
Subproblem 2
Set the factor '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

Solving
5 + y = 0

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

Add '-5' to each side of the equation.
5 + -5 + y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + y = 0 + -5
y = 0 + -5

Combine like terms: 0 + -5 = -5
y = -5

Simplifying
y = -5
Solution
y = {-7, -5}