(k+3)(k+5)=0

Solution for (k+3)(k+5)=0 equation:

Simplifying
(k + 3)(k + 5) = 0

Reorder the terms:
(3 + k)(k + 5) = 0

Reorder the terms:
(3 + k)(5 + k) = 0

Multiply (3 + k) * (5 + k)
(3(5 + k) + k(5 + k)) = 0
((5 * 3 + k * 3) + k(5 + k)) = 0
((15 + 3k) + k(5 + k)) = 0
(15 + 3k + (5 * k + k * k)) = 0
(15 + 3k + (5k + k2)) = 0

Combine like terms: 3k + 5k = 8k
(15 + 8k + k2) = 0

Solving
15 + 8k + k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(5 + k)(3 + k) = 0

Subproblem 1
Set the factor '(5 + k)' equal to zero and attempt to solve:

Simplifying
5 + k = 0

Solving
5 + k = 0

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

Add '-5' to each side of the equation.
5 + -5 + k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + k = 0 + -5
k = 0 + -5

Combine like terms: 0 + -5 = -5
k = -5

Simplifying
k = -5
Subproblem 2
Set the factor '(3 + k)' equal to zero and attempt to solve:

Simplifying
3 + k = 0

Solving
3 + k = 0

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

Add '-3' to each side of the equation.
3 + -3 + k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + k = 0 + -3
k = 0 + -3

Combine like terms: 0 + -3 = -3
k = -3

Simplifying
k = -3
Solution
k = {-5, -3}