Find $a,b,c,d,e,f,g,h \in \mathbb{R}$ such that
$$ (x+2y+3)(ax+by+cz+d) + (y+z+2)(ex+fy+gz+h) + x+y+z = (ax+by+cz+d)(ex+fy+gz+h)$$
holds in $\mathbb{R}[x,y,z]$.
Is there a $``$good$"$ way for this? Or is there a calculator or afunction in Wolfram Mathematica that can do this automatically?
Any help appreciated!