Let's solve the equation step by step:

\[
X(x+1) - (x-2)(x+2) = 0
\]

First, expand the left-hand side of the equation:

1. Expand \( (x-2)(x+2) \) using the difference of squares formula:

\[
(x-2)(x+2) = x^2 - 4
\]

2. Now, substitute this back into the equation:

\[
X(x+1) - (x^2 - 4) = 0
\]

3. Distribute \(X\):

\[
Xx + X - x^2 + 4 = 0
\]

4. Rearrange the equation to set it to zero:

\[
Xx + X - x^2 + 4 = 0
\]
Now, we can group the terms:

\[
-x^2 + Xx + X + 4 = 0
\]

Reordering gives:

\[
-x^2 + Xx + (X + 4) = 0
\]

Now, if \(X\) represents an unknown constant (which was unclear in the initial problem statement), the equation can be further solved depending on the context. However, if \(X\) is just a coefficient or if we assume it represents a variable we need to isolate, the nature of solving will change.

Please clarify if \(X\) is a specific number or if you are setting it to some value so we can proceed with specific steps or solutions based on that context.