(k+5)(k+2)=0

Solution for (k+5)(k+2)=0 equation:

Simplifying
(k + 5)(k + 2) = 0

Reorder the terms:
(5 + k)(k + 2) = 0

Reorder the terms:
(5 + k)(2 + k) = 0

Multiply (5 + k) * (2 + k)
(5(2 + k) + k(2 + k)) = 0
((2 * 5 + k * 5) + k(2 + k)) = 0
((10 + 5k) + k(2 + k)) = 0
(10 + 5k + (2 * k + k * k)) = 0
(10 + 5k + (2k + k2)) = 0

Combine like terms: 5k + 2k = 7k
(10 + 7k + k2) = 0

Solving
10 + 7k + k2 = 0

Solving for variable 'k'.

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

Simplifying
2 + k = 0

Solving
2 + k = 0

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

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

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

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

Simplifying
k = -2
Solution
k = {-5, -2}