|6s+9|=|s+7|, square both sides:
(6s+9)2=(s+7)2,
(6s+9)2-(s+7)2=0,
(6s+9+s+7)(6s+9-s-7)=0,
(7s+16)(5s+2)=0, s=-16/7 or s=-2/5.
CHECK
|-96/7+9|=|-16/7+7|, |(-96+63)/7|=|(-16+49)/7|, |-33/7|=|33/7|✔️
|-12/5+9|=|-2/5+7|, |(-12+45)/5|=|(-2+35)/5|, |33/5|=|33/5|✔️