I don't understand why the following non-homogeneous equation has been solved as shown below:
$h(x) = 1 + ph(x-1) + (1-p)h(x+1)$
Let $h(x) = Rx$
Hence, $Rx = 1 + pR(x-1) + (1-r)R(x+1)$
Which gives, $R = \frac{1}{2p - 1}$ Hence $h = \frac{x}{2p - 1}$
I don't understand how $R$ was obtained to be as such and why $h(x) = Rx$ was substituted into the first equation.
Thank You