Euclidean algorithm to find the GCD I have to find the greatest common divisor of $a=78$ and $b=132$.
I have worked out to
$$\begin{align}
132 & = 78 \times 1 + 54 \\
78 & = 54 \times 1 + 24 \\
54 & = 24 \times 2 + 6 \\
24 & = 6 \times 4 + 0
\end{align}$$
and back substituted
$$\begin{align}
6 & = 54 - 24 \times 2 \\
  & = 54 - (78 - 54) \times 2 \\
  & = 3 \times 54 - 78 \times 2 
\end{align}$$
However I don't seem to be able to work back to $132$ ? 
Can someone explain / help?

From the first equation you have $54=132-78$. 
By plugging this into the last one you get $6=3(132-78)-2\cdot78=3\cdot132-5\cdot78.$
