elementary number theory - Find the Inverse Modulus using Euclid's algorithm

I asked this before, but unfortunately, I didnt know the methods, nor was the questions phrased properly.

Find the inverse of $4258 \pmod{147}$ Using Euclidean Extended Algorithm.

Begin By Stating the remainders (Euclid's Algorithm):

$4258 = 28(147) + 142$

$147 = 1(142) + 5$

$142 = 28(5) + 2$

$5 = 2(2) + 1$

Then BACK substitution starting with $1$:

$1 = 5 - 2\cdot 2$

$1 = 5 - 2\cdot \bigg(142 - 28(5)\bigg ) = -279 + 2\cdot 28(5)$

$1 = -279 + 2\cdot 28\bigg( 147 - 142 \bigg)$

$1 = -279 + 56 \cdot \bigg( 147 - 4258 + 28(147) \bigg)$

But how would I proceed?