(y+8)(y+1)=0

Solution for (y+8)(y+1)=0 equation:

Simplifying
(y + 8)(y + 1) = 0

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

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

Multiply (8 + y) * (1 + y)
(8(1 + y) + y(1 + y)) = 0
((1 * 8 + y * 8) + y(1 + y)) = 0
((8 + 8y) + y(1 + y)) = 0
(8 + 8y + (1 * y + y * y)) = 0
(8 + 8y + (1y + y2)) = 0

Combine like terms: 8y + 1y = 9y
(8 + 9y + y2) = 0

Solving
8 + 9y + y2 = 0

Solving for variable 'y'.

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

Subproblem 1
Set the factor '(8 + y)' equal to zero and attempt to solve:

Simplifying
8 + y = 0

Solving
8 + y = 0

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

Add '-8' to each side of the equation.
8 + -8 + y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + y = 0 + -8
y = 0 + -8

Combine like terms: 0 + -8 = -8
y = -8

Simplifying
y = -8
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 = {-8, -1}