(k+3)(k-2)=24

Solution for (k+3)(k-2)=24 equation:

Simplifying
(k + 3)(k + -2) = 24

Reorder the terms:
(3 + k)(k + -2) = 24

Reorder the terms:
(3 + k)(-2 + k) = 24

Multiply (3 + k) * (-2 + k)
(3(-2 + k) + k(-2 + k)) = 24
((-2 * 3 + k * 3) + k(-2 + k)) = 24
((-6 + 3k) + k(-2 + k)) = 24
(-6 + 3k + (-2 * k + k * k)) = 24
(-6 + 3k + (-2k + k2)) = 24

Combine like terms: 3k + -2k = 1k
(-6 + 1k + k2) = 24

Solving
-6 + 1k + k2 = 24

Solving for variable 'k'.

Reorder the terms:
-6 + -24 + 1k + k2 = 24 + -24

Combine like terms: -6 + -24 = -30
-30 + 1k + k2 = 24 + -24

Combine like terms: 24 + -24 = 0
-30 + 1k + k2 = 0

Factor a trinomial.
(-6 + -1k)(5 + -1k) = 0

Subproblem 1
Set the factor '(-6 + -1k)' equal to zero and attempt to solve:

Simplifying
-6 + -1k = 0

Solving
-6 + -1k = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1k = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1k = 0 + 6
-1k = 0 + 6

Combine like terms: 0 + 6 = 6
-1k = 6

Divide each side by '-1'.
k = -6

Simplifying
k = -6
Subproblem 2
Set the factor '(5 + -1k)' equal to zero and attempt to solve:

Simplifying
5 + -1k = 0

Solving
5 + -1k = 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 + -1k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1k = 0 + -5
-1k = 0 + -5

Combine like terms: 0 + -5 = -5
-1k = -5

Divide each side by '-1'.
k = 5

Simplifying
k = 5
Solution
k = {-6, 5}