なくて済む/ないで済む => get by without doing ~ N2
を[経「へ」]て => After A N1
Time, Situation
全く~ない => not at all ~ N3
全然~ない => (not) at all N4
~をたて(~を経て)      => through; after; via N1
ずに済む => get by without doing ~ N2
て済む => sufficient by; no problem to; resolve by ~ N3
[全「まった」]く~ない => Not A (at all; even a little bit) N3
Not only, Not even