(2k+5)(3k+8)=0

Solution for (2k+5)(3k+8)=0 equation:

Simplifying
(2k + 5)(3k + 8) = 0

Reorder the terms:
(5 + 2k)(3k + 8) = 0

Reorder the terms:
(5 + 2k)(8 + 3k) = 0

Multiply (5 + 2k) * (8 + 3k)
(5(8 + 3k) + 2k * (8 + 3k)) = 0
((8 * 5 + 3k * 5) + 2k * (8 + 3k)) = 0
((40 + 15k) + 2k * (8 + 3k)) = 0
(40 + 15k + (8 * 2k + 3k * 2k)) = 0
(40 + 15k + (16k + 6k2)) = 0

Combine like terms: 15k + 16k = 31k
(40 + 31k + 6k2) = 0

Solving
40 + 31k + 6k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(8 + 3k)(5 + 2k) = 0

Subproblem 1
Set the factor '(8 + 3k)' equal to zero and attempt to solve:

Simplifying
8 + 3k = 0

Solving
8 + 3k = 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 + 3k = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3k = 0 + -8
3k = 0 + -8

Combine like terms: 0 + -8 = -8
3k = -8

Divide each side by '3'.
k = -2.666666667

Simplifying
k = -2.666666667
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 = {-2.666666667, -2.5}