(2k-5)(3k+6)=0

Solution for (2k-5)(3k+6)=0 equation:

Simplifying
(2k + -5)(3k + 6) = 0

Reorder the terms:
(-5 + 2k)(3k + 6) = 0

Reorder the terms:
(-5 + 2k)(6 + 3k) = 0

Multiply (-5 + 2k) * (6 + 3k)
(-5(6 + 3k) + 2k * (6 + 3k)) = 0
((6 * -5 + 3k * -5) + 2k * (6 + 3k)) = 0
((-30 + -15k) + 2k * (6 + 3k)) = 0
(-30 + -15k + (6 * 2k + 3k * 2k)) = 0
(-30 + -15k + (12k + 6k2)) = 0

Combine like terms: -15k + 12k = -3k
(-30 + -3k + 6k2) = 0

Solving
-30 + -3k + 6k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + -1k + 2k2) = 0

Factor a trinomial.
3((-2 + -1k)(5 + -2k)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + -1k)' equal to zero and attempt to solve:

Simplifying
-2 + -1k = 0

Solving
-2 + -1k = 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 + -1k = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1k = 0 + 2
-1k = 0 + 2

Combine like terms: 0 + 2 = 2
-1k = 2

Divide each side by '-1'.
k = -2

Simplifying
k = -2
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, 2.5}