This is the last of the moment-generating function problems that I do not understand for our homework. Any help would be greatly appreciated. Thanks!

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