if we're changing the subject to t, we want to get t on it's own.
S = P(1 + rt)
Since we can't do anything with the parenthesis, we have to start with the division/multiplication. Divide both sides by P:
S = 1 + rt
P
Next we want to get rid of the 1, so subtract 1 from both sides:
S - 1 = rt
P
finally, divide both sides by r
(S/P) - 1 = t
r
so:
t = (S/P) - 1
r
