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

To solve the inequality \( X^2 - (X + 6)(X - 6) > 12X \), we first simplify the expression.

1. Expand \( (X + 6)(X - 6) \): \[ (X + 6)(X - 6) = X^2 - 36 \]

2. Substitute this back into the inequality: \[ X^2 - (X^2 - 36) > 12X \]

3. Simplify the left side: \[ X^2 - X^2 + 36 > 12X \] This simplifies down to: \[ 36 > 12X \]

4. Now, solve for \( X \) by dividing both sides by 12: \[ 3 > X \quad \text{or} \quad X < 3 \]

Thus, the solution to the inequality \( X^2 - (X + 6)(X - 6) > 12X \) is: \[ X < 3 \]

Therefore, the solution set is: \[ (-\infty, 3) \]