(y+5)(y+1)=0

Solution for (y+5)(y+1)=0 equation:

Simplifying
(y + 5)(y + 1) = 0

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

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

Multiply (5 + y) * (1 + y)
(5(1 + y) + y(1 + y)) = 0
((1 * 5 + y * 5) + y(1 + y)) = 0
((5 + 5y) + y(1 + y)) = 0
(5 + 5y + (1 * y + y * y)) = 0
(5 + 5y + (1y + y2)) = 0

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

Solving
5 + 6y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(5 + y)(1 + y) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

Solving
1 + y = 0

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 + -1

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

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

Simplifying
y = -1
Solution
y = {-5, -1}