Therefore, I used the equation t1/2=1/k[A]0 solved for K with the t/12=30 and [A]0=0.840
But t1/2 is not 30, is it? It's 15, as you can see from your data.
You may say: "But the concentration drops from 0.42 to 0.21 over 30 minutes." Yes, but [A]0 for that period is 0.42, not 0.84.
The point is that for a 2nd order reaction, unlike a 1st order one, the half life depends on the initial concentration, and therefore changes during the reaction. The second half-life is twice as long as the first, and the third twice as long as the second, and so on. The third half life will be 60 min, and the concentration will be 0.105 M after 105 min.
That's why you need to be careful about using half-lives to calculate k for non-first-order reactions. Better to use the slope of the 1/[A] vs t curve. This is also likely to be better if it involves more than 2 data points.