Find values that put equation to zero

In this model:

where all the variables are of dymension TX1, I need to find all the (T) values of gamma that put the equation to zero.

I tryed with the following code, but the program returns me all NAN, how can I fix the code to get it?

j=1; %increment level. The loop will work for j>1 as well.
for i=1:j:T;
fnc = @(gamma,C,S) 1./(1+gamma).*(C(i)-(S(i)*gamma)) - M(i);  % Model function
rn = @(gamma) norm(M - fnc(gamma,C,S)); % Residual norm
gamma0 = [15]; % Inizializzazione
[gamma, ResNorm] = fzero(rn, gamma0);  
end

Answer 1

[Matt J]

gamma=nan(T,1);

j=1; %increment level. The loop will work for j>1 as well.
for i=1:j:T;
    
  ci=C(i); si=S(i); mi=M(i);
   
  fnc = @(gamma) 1./(1+gamma).*(ci-(si*gamma)) - mi;  

  gamma0 = 15; 
  
  [gamma(i), ResNorm] = fzero(fcn, gamma0);  

end

[MARCO FORTI]

It still returns me NaN

[Matt J]

You may be initializing at a bad point. This works:

T=5;
[C,S,M]=deal(rand(T,1), rand(T,1), rand(T,1));

gamma=nan(T,1);

j=1; %increment level. The loop will work for j>1 as well.
for i=1:j:T;
    
  ci=C(i); si=S(i); mi=M(i);
   
  fnc = @(gamma) 1./(1+gamma).*(ci-(si*gamma)) - mi;  

  gamma0 = 15; 
  
  [gamma(i), ResNorm] = fzero(fnc, 0);  

end

gamma

gamma = 5×1

-1.0000 0.0302 0.6949 0.1094 -0.4440

[MARCO FORTI]

It works, thanks!

Answer 2

[Alan Stevens]

If your expression is equal to zero, then you can rearrange it to get gamma directly. A little algebra gives

gamma = (C-M)./(S+M);

No need for fzero at all.

[MARCO FORTI]

Sorry, I mispelled the formula, now I corrected fixed it.

However I would like to understand how to develope a proper matlab code for this (or other similar) situations. Could you help?