1. Moment generating function problem

Hello this is my first post in this forum. I hope I can give back some help in my spare time. I'll go on with my question.

Given the moment generating function $M_x (t) = e^{3t + 8t^2 }$ , find the moment generating function of the random variable $Z = \frac{1}
{4}(X - 3)$
, and use it to determine the mean and the variance of Z.

I am a quite confused since I don't know exactly what are they asking from me. The only thing that closely resembles an answer that I have come up with is to calculate $\mu$ and $\sigma ^2$ using the given generating function and use the standard deviation obtained as the integration limits for finding the mgf of Z. If my approach ok? I'm i totally wrong?

Edit: I should probably add that I calculated the mean and sd and arrived at a mean of 3 and sd of 4. This just doesn't seem right to me.