Is there any way to solve the integration below? or make it simple to eliminate the Dirac-delta function?

$$\int\_{-\infty}^\infty m(x)\delta(G(x)-g\_c)f\_X(x)dx $$

where $f\_X(x)$ is a probability density function (PDF) of random variable x.

It will be very helpful for any reference or clue to solve it.

Thank you.