(r+2)(r+8)=0

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

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

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

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

Multiply (2 + r) * (8 + r)
(2(8 + r) + r(8 + r)) = 0
((8 * 2 + r * 2) + r(8 + r)) = 0
((16 + 2r) + r(8 + r)) = 0
(16 + 2r + (8 * r + r * r)) = 0
(16 + 2r + (8r + r2)) = 0

Combine like terms: 2r + 8r = 10r
(16 + 10r + r2) = 0

Solving
16 + 10r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(8 + r)(2 + r) = 0

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

Simplifying
8 + r = 0

Solving
8 + r = 0

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

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

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

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

Simplifying
r = -8
Subproblem 2
Set the factor '(2 + r)' equal to zero and attempt to solve:

Simplifying
2 + r = 0

Solving
2 + r = 0

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

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

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

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

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