First, add #color(red)(10)# and #color(blue)(2m)# to each side of the equation to isolate the #m# term while keeping the equation balanced:
#8m - 10 + color(red)(10) + color(blue)(2m) = 5 - 2m + color(red)(10) + color(blue)(2m)#
#8m + color(blue)(2m) - 10 + color(red)(10) = 5 + color(red)(10) - 2m + color(blue)(2m)#
#(8 + color(blue)(2))m - 0 = 15 - 0#
#10m = 15#
Now, divide each side of the equation by #color(red)(10)# to solve for #m# while keeping the equation balanced:
#(10m)/color(red)(10) = 15/color(red)(10)#
#(color(red)(cancel(color(black)(10)))m)/cancel(color(red)(10)) = (5 xx 3)/color(red)(5 xx 2)#
#m = (color(red)(cancel(color(black)(5))) xx 3)/color(red)(color(black)(cancel(color(red)(5))) xx 2)#
#m = 3/2#