I need to simplify the following convolution
$$x(t)\star [e^{-2t} u(t)]$$
where $u(t)$ is the unit step function. I'm very confused with this. Using the definition of convolution of continuous-time signals, I obtained
$$\int\limits_{-\infty}^t {x(\tau)e^{-2(t-\tau)}u(t-\tau)}{d\tau} $$
However, I have no idea what to do at this step. I'm stuck. Is there any property / theorem / trick that can help me simplify this?