X*X-(X+6)(X-6)>12X

To solve the inequality \( X^2 - (X + 6)(X - 6) > 12X \), let's first simplify the left-hand side.

We can start by expanding \( (X + 6)(X - 6) \):

\[ (X + 6)(X - 6) = X^2 - 36 \]

Now, substituting this back into the inequality, we have:

\[ X^2 - (X^2 - 36) > 12X \]

This simplifies to:

\[ X^2 - X^2 + 36 > 12X \]

or

\[ 36 > 12X \]

Next, we'll rearrange the inequality:

\[ 36 - 12X > 0 \]

This can be rewritten as:

\[ 12X < 36 \]

Now, divide both sides by 12:

\[ X < 3 \]

Thus, the solution to the inequality is:

\[ X < 3 \]

In interval notation, the solution is \( (-\infty, 3) \).