Intelligent symbolic variable substitution

EDIT: I created an example to specify my problem in more detail.

I want to substitute variables in an equation system. Here an example to illustrate my idea:

syms f(x) z(x)
fun1 = f == (x+4)^2 + 4;    % equals (x+4)^2
fun2 = f == x^2+8*x+20;    % equals (x+4)^2
% fun1 === fun2
transform = z == (x+4)^2;
subs(fun1, rhs(transform), lhs(transform)) % Results in z(x) + 4
subs(fun2, rhs(transform), lhs(transform)) % Results in x^2 + 8x + 20

Obviously, fun1 and fun2 are the same. However Matlab is not able to replace the expression for z correctly when given in the form of fun2. Is there a way to achieve the same result in both notations?

Thank you for your help in advance.

Answer 1

[Stephan]

syms f(x) z(x)
fun = f == x^2 + 8*x + 16;    % equals (x+4)^2
transform = z == (x+4)^2;
subs(fun, rhs(fun), lhs(transform))

[Arjun Sarin]

Thank you for your answer! Could you please elaborate what's the difference in the code? You are using symbolic functions which I didn't but I don't get my mistake...

[Stephan]

You could also use:

syms f x z
fun = f == x^2 + 8*x + 16;    % equals (x+4)^2
transform = z == (x+4)^2;
subs(fun, rhs(fun), lhs(transform))

The idea is declaring f the same way like transform - which you did not do. Thats all.

[Arjun Sarin]

Thank you again. I tried the different notations in depth but actually it doesn't work for me. I updated the questions as the above.