Transform polynomium equation into multiple coefficient equations

Hello

I want to match coefficients from 2 polynomiums:

syms x 
syms a [3,1]
syms alpha beta gamma

eq = (1-alpha)*x^2 + (1-beta)*x + (1-gamma) == a1 *x^2 + 0*x + a3 

Such that i get:

>>eq1 = 1-alpha == a1
>>eq2 = 1-beta == 0
>>eq3 = 1-gamma == a3

My current solution is:

cL = coeffs(lhs(eq),x,'all');
cR = coeffs(rhs(eq),x,'all');

new_eq = cL == cR

But that does not work when x is raised to a negative power:

eq = (1-alpha)*x^-2 + (1-beta)*x^-1 + (1-gamma) == a1 *x^-2 + 0*x^-1 + a3 

I know that i can make a placeholder variable such that:

syms z
eq = subs(eq,x^-1,z)

cL = coeffs(lhs(eq),z,'all');
cR = coeffs(rhs(eq),z,'all');

new_eq = cL == cR

But that does not work if i have x to both positive and negative powers. And i am wondering if there is a command that can do all that for me instead