Answer
Basic reason: zero product principle.
please see "step by step for details"
Work Step by Step
The reason is: the zero product principle.
(in short: if one factor is 0, the whole product is zero)
(also, if the product is zero, then (at least) one of the factors is zero)
The polynomial equation $f(x)=0$ has n factors on the LHS.
For the equation $f(x)=0$ to be satisfied, a factor on the LHS must be 0.
There are n factors, and any one may be 0, so
the solution set is
$\{c_{1}, c_{2}, ..., c_{n}\}$
which has n members.
The above set represents the n zeros of f(x), that is the n values of x for which f(x)=0.
Each of the n zeros of the polynomial f(x) is a root (solution) of the equation f(x)=0.
