How can I find the multiplicative inverse of $7 \pmod{15}$?

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I tried, although didn't succeed. I got to the point where I have got $15 = 7 \cdot 2 + 1$. And then I have rearranged this for $1$.

In addition, is there a general way to solve these?

Thanks.

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If you know $$15=7(2)+1$$

Let's consider $\mod 15$

$$0\equiv7(2)+1 \mod 15$$

$$7(-2) \equiv 1 \mod 15$$

Hence $$(13)7\equiv 1 \mod 15$$