analysis – de-meaned data of dependent variable

A book on financial econometrics states:

we could subtract the mean from the data and write factor models in terms of de-meaned data x on y

= −µ µ where is the mean of y.
In this case, the constant terms a i are all equal to zero.

This does not appear evident. y is a dependent variable. If we substract its mean, we should get residuals, not x. Could ye please advise, on what logick foundation does the de-meaned data rest? Thank ye.