I ended up getting xe^-2x [ 2 - 2x ] but how do I set this equal to 0 to find the intervals of increase and decrease?
From the null factor law: $\displaystyle xe^{-2x} (2 - 2x) = 0 \Rightarrow$ $\displaystyle x = 0$ or $\displaystyle 2 - 2x = 0$. Note that one of the solutions does NOT correspond to a turning point.