(2k+5)(k+3)=0

Solution for (2k+5)(k+3)=0 equation:

Simplifying
(2k + 5)(k + 3) = 0

Reorder the terms:
(5 + 2k)(k + 3) = 0

Reorder the terms:
(5 + 2k)(3 + k) = 0

Multiply (5 + 2k) * (3 + k)
(5(3 + k) + 2k * (3 + k)) = 0
((3 * 5 + k * 5) + 2k * (3 + k)) = 0
((15 + 5k) + 2k * (3 + k)) = 0
(15 + 5k + (3 * 2k + k * 2k)) = 0
(15 + 5k + (6k + 2k2)) = 0

Combine like terms: 5k + 6k = 11k
(15 + 11k + 2k2) = 0

Solving
15 + 11k + 2k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(3 + k)(5 + 2k) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + 2k)' equal to zero and attempt to solve:

Simplifying
5 + 2k = 0

Solving
5 + 2k = 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 + 2k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2k = 0 + -5
2k = 0 + -5

Combine like terms: 0 + -5 = -5
2k = -5

Divide each side by '2'.
k = -2.5

Simplifying
k = -2.5
Solution
k = {-3, -2.5}