(k+1)(k+8)=0

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

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

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

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

Multiply (1 + k) * (8 + k)
(1(8 + k) + k(8 + k)) = 0
((8 * 1 + k * 1) + k(8 + k)) = 0
((8 + 1k) + k(8 + k)) = 0
(8 + 1k + (8 * k + k * k)) = 0
(8 + 1k + (8k + k2)) = 0

Combine like terms: 1k + 8k = 9k
(8 + 9k + k2) = 0

Solving
8 + 9k + k2 = 0

Solving for variable 'k'.

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

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

Simplifying
8 + k = 0

Solving
8 + k = 0

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

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

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

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

Simplifying
k = -8
Subproblem 2
Set the factor '(1 + k)' equal to zero and attempt to solve:

Simplifying
1 + k = 0

Solving
1 + k = 0

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

Add '-1' to each side of the equation.
1 + -1 + k = 0 + -1

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

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

Simplifying
k = -1
Solution
k = {-8, -1}