If $X\sim\chi^2_{df=6}$, what is the probability density function of $T = \frac{(X-6)}{\sqrt12}$?

The problem I'm confronted with is that the chi-squared random variable, $X$, can assume only positive values while the random variable $T$ can assume both positive and negative values.

I tried to use both the PDF technique and the CDF technique for transformations of random variables but in the end the PDF of $T$ could assume only positive values, that is my problem.