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To solve the inequality (x+2)(x-3) < 0, we can use the concept of the sign chart.

First, let's find the critical points by setting each factor equal to zero:

x + 2 = 0
x = -2

x - 3 = 0
x = 3

Now, we can create a sign chart using these critical points:

-∞ -2 3 +∞
--------------------
(x+2) - 0 + +
(x-3) - - 0 +
--------------------
- + - +

In the intervals (-∞, -2), (-2, 3), and (3, +∞), we can see the signs of each factor:

(x+2) is negative in (-∞, -2) and positive in (-2, +∞).
(x-3) is negative in (-∞, 3) and positive in (3, +∞).

To determine the sign of the product (x+2)(x-3), we can look at the sign chart. The product is negative when the factors have opposite signs.

Therefore, the solution to the inequality (x+2)(x-3) < 0 is:

-2 < x < 3