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

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

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

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

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

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

Combine like terms: 2k + -3k = -1k
(-6 + -1k + k2) = 0

Solving
-6 + -1k + k2 = 0

Solving for variable 'k'.

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

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 '(3 + -1k)' equal to zero and attempt to solve:

Simplifying
3 + -1k = 0

Solving
3 + -1k = 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 + -1k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1k = 0 + -3
-1k = 0 + -3

Combine like terms: 0 + -3 = -3
-1k = -3

Divide each side by '-1'.
k = 3

Simplifying
k = 3
Solution
k = {-2, 3}