# Solve symbolic equation by comparing coefficients

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Jörn Froböse on 9 Feb 2022
Commented: Jörn Froböse on 17 Feb 2022
I have an equation like this: , which I need to rearrange to this form: .
Obviously, the above holds true for and . However, I would like to do this automatically. How can d and e be found using Matlabs Symbolic Toolbox?
The following approach won't help, since the system isn't well defined.
syms a b c d e f x y z
eq = a*x + y*(b + c*z)==0;
target = x + y*(d + e*z)==0;
solve([eq target],[d e])
Any help would be appreciated!
##### 2 CommentsShowHide 1 older comment
Jörn Froböse on 10 Feb 2022
Hey Highphi, thank you for your suggestion. This would'nt be really helpful in my case, since I need coefficients d and e without any dependence on x, y and z. I kind of solved it now by "brute-forcing" and using subs.

Prachi Kulkarni on 15 Feb 2022
Edited: Prachi Kulkarni on 15 Feb 2022
Hi,
For a given example expression of the form a*x + y*(b + c*x), you can get the coefficients d and e of the reduced forms as follows.
syms x y z
eq = 2*x + y*(3 + 4*z); % input equation
[d,e] = reducedCoefficients(eq);
function [d,e] = reducedCoefficients(eq)
coef = coeffs(eq);
b = coef(1);
c = coef(2);
a = coef(3);
d = double(b/a);
e = double(c/a);
end
Jörn Froböse on 17 Feb 2022
Thank you, this works for me!