2 Find all integer $x$ such that $\left|4 x^{2}-12 x-27\right|$ is a prime number.

Find all integer $x$ such that $\left|4 x^{2}-12 x-27\right|$ is a prime number.
2. From $\left|4 x^{2}-12 x-27\right|=|(2 x+3)(2 x-9)|$, we know that only when $|2 x+3|=1$ or $|2 x-9|=1$, the number $\left|4 x^{2}-12 x-27\right|$ can possibly be a prime number. According to this, the required $x=-2,-1,4$ or 5, and the corresponding $\left|4 x^{2}-12 x-27\right|$ are 13, 11, 11 or 13, all of which are prime numbers.