Is $O(f(n)\cdot g(n)) = f(n)\cdot O(g(n))$?

Question

Prove or disprove with counter example:
$$O(f(n)\cdot g(n)) = f(n)\cdot O(g(n))$$

Attempt:
$f(n) = x^2 + x + 1$
$g(n) = x^3$
L.H.S. = $x^5$
R.H.S. = $(x^2 + x + 1)x^3$
L.H.S. $\neq$ R.H.S.

Am i correct?