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Find the solutions to $4x \equiv 16 \pmod{20}$

I managed to determine this by writing $4x = 16 + 20j \implies x =4 +5j \implies x \equiv 4 \pmod{5}$, but the official solution stated that the solutions are $x = 4,9,14,19 \pmod{20}$ which I'm not entirely sure how they got?

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    As in the proof in the linked dupe, using $\rm\color{#c00}{mDL}$ = mod Distributive Law we have

    $$\large \begin{align}\bmod 20!:\ x &\equiv 4+5j \ &\equiv 4 + (5j\bmod 20)\ &\equiv 4 + 5(\color{#0a0}{j\bmod 4})\ \ {\rm by},\ \rm\color{#c00}{mDL}\ &\equiv 4 + 5\color{#0a0}{{0,1,2,3}}\ &\equiv 4,,9,,14,,19 \end{align}\qquad\qquad$$

     – Bill Dubuque Feb 23 '21 at 09:49
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    Your solution and the official solution are the same! – anon Feb 23 '21 at 09:58

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