Is it possible to open up this particular convolution equation?
Here is a re-write of a previously mistaken answer:

Let us write $y[n] = z[n] * \Big(x[n] \cdot w[n] \Big) = \displaystyle\sum_{m=-M}^{M} {z[n-m] \cdot (x[m] \cdot w[m])}$ and rearrange as $y[n] = \displaystyle\sum_{m=-M}^{M} {(z[n-m] \cdot x[m]) \cdot (w[m])}$. After this point, we cannot take the terms out of the brackets.