The problem is "guessing" at all! The only reason c, in s= c+ mt is not "by itself" already is that mt is added to it. To "undo" that, do the opposite: the opposite of "add mt" is "subtract mt". Subtract mt from both sides to get s-mt= c which is the same as c= s- mt.
Now, t, in s= c+ mt is not "by itself" is that two things have been done to it: to get to "c+ mt" from t, you would "multiply by m" and "add c" in that order. To "undo" it, do the opposite things in the opposite order: first "subtract c" then "divide by t".
From s= c+ mt, subtracting c from both sides gives s- c= mt. Now divide both sides by m- but be sure to show that the entire right side, s- c, is divided by m, not just "c": use parentheses (s-c)/m= t, not "s- c/m" which means s- (c/m)!