number theory - Solving for Modular arithmetic

Solve the equation $38z\equiv 21 \pmod {71}$ for z.
Little confused by the questions. My attempt is: $38 \odot z = 21.$ Then find the inverse of 38 from mod 71 and multiply both sides. Lastly, take the mod of RHS and solve for z. I could find the inverse of 38 by solving for the following: $gcd(38,21)=38x+21y=1.$ But this is somewhat a long process. First of all, am I thinking of computing the problem the write way? If so, is there a shorter algorithm for computing for the inverse of 38 instead of solving for $38x+21y=1?.$