(y+2)(y+8)=0

Solution for (y+2)(y+8)=0 equation:

Simplifying
(y + 2)(y + 8) = 0

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

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

Multiply (2 + y) * (8 + y)
(2(8 + y) + y(8 + y)) = 0
((8 * 2 + y * 2) + y(8 + y)) = 0
((16 + 2y) + y(8 + y)) = 0
(16 + 2y + (8 * y + y * y)) = 0
(16 + 2y + (8y + y2)) = 0

Combine like terms: 2y + 8y = 10y
(16 + 10y + y2) = 0

Solving
16 + 10y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(8 + y)(2 + 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 '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

Solving
2 + y = 0

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

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

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

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

Simplifying
y = -2
Solution
y = {-8, -2}