How do you solve quadratic congruences with unknown modulo using Chinese Remainder Method and Hensel's Lemma

Question

Show that for all positive integers $n$, the following congruence has solutions: $$(x^2-2)(x^2+7)(x^2+14) \equiv 0 \pmod{n}$$ I need to use the Chinese Remainder Theorem and Hensel’s Lemma. So far I have shown that using for all primes where $p$ does not equal $7$ or $2$ we have $(2/p)$, $(-7/p)$, $(-14/p) = 1$, however I'm not sure how to use the Chinese remainder theorem. I understand you would need to factorise and complete the square usually but not sure how to solve this question. I would appreciate any help.