## How to solve an equation with element-wise multiplication?

I need to solve an equation that involves matrix element-wise multiplication, as follows:

x.*Ax = Bx,
where x is a vector, ".*" is element-wise multiplication (i.e., multiply element-by-element), A and B are non-negative matrices.

I just don't know where to start because I don't know any properties of element-wise multiplication. Could any one give me some hints about it?

Thanks