$A $, $ C$ $(n,n)$ are symmetric PSD matrices, $B$ is PD symmetric matrix, and $H_i$ $\; $ $(i=[1,m])$ represent $ m $ complex matrices. $H_i$ are all one rank matrix

Our objectif is to find PSD matrix X that enable:

$A\sum\limits_{i = 1}^{m - 1} {{H_i}(B + X){H_i} + A(X + B) + {H_m}(B + X) = C}$