How would you solve this problem algebraically

Here is the problem:

Giancarlo has two more than three times the number of baseball cards that Antonio has. If Giancarlo gave Antonio 12 of his cards, they would each then have the same number of cards. How many cards does Giancarlo have?

I solved it using a table, and got that Giancarlo started out with 35 cards, and when he gives 12 to Antonio they both would have 23. So now I need to solve it algebraically, any ideas?

First sentence translates to G = 3A+2, with G = Giancarlo's cards and A = Antonio's cards.

G - 12 = A + 12 Second sentence. G would have 12 fewer cards and A would have 12 more cards.

G = 3A+2 and G-12=A+12, so 3A+2-12=A+12 (substituting the 3A+2 for G).

3A-10=A+12
2A=22
A=11

Antonio started with 11 cards, which means Giancarlo began with 3x11+2 or 35 cards.

35-12=23 and 11+12=23

yes this is correct. To show it algebraically
Consider that Antonio had x cards in the beginning then the no of cards with Giancarlo was 3x+2

now adding 12 cards to Antonio and subtracting 12 cards from Giancarlo will result into both of them having same no of cards which means that

x+12=3x+2-12
after solving this you will get the value of x as 11

Giancarlo's cards x, Antonio's y
x-12 = y+12 (give 12 cards from G to A)
x - 2 = 3y (reducing G's by 2 is 3 times A's)
x = 3y+2
3y+2 -12 = y+12
so y = 11
x = 35