continuing congruence equation

Question

How do you solve this congruence equation?
$$3\equiv -4a\pmod {13}$$
What I did was :
Applying symmetry property
$$ -4a\equiv 3\pmod {13} $$ Since gcd(13,4) = 1 we multiply both sides by inverse of $4\pmod {13}$
$$-a\equiv30\pmod{13}$$ $$a\equiv-30\pmod{13}$$ How can I continue from this point? $ a + 30 = 13k$ doesn't help me.

Answer 1

more handy solution:
3 = -4a (mod 13)
9 = -12a (mod 13)
9 = a (mod 13) <--i think you could figure it out.

so , a = 9, 21,......

Answer 2

What I didn't know was that $-30\pmod{13} =9 $ is not equal to $30\pmod{13}=4$
So we can write the above expression as $$ a\equiv9\pmod{13}$$ $$ a = 9$$