Balance the equation:

Note: If a chemical species coefficient is "1" then "1" needs to be entered in the field before that species.
MnO4– + H+ + Fe2+ Mn2+ + H2O + Fe3+

If you want to do it by half reactions, the half reactions are as follows:

MnO4^- ==> Mn^+2
Fe+2 ==> Fe^+3

If you want to do it the shorter way, the oxidation state of Mn changes from +7 on the left to +2 on the right. The oxidation state of Fe changes from +2 on the left to +3 on the right.
[Note: technically, this equation can't be balanced because you didn't include an arrow. I KNOW where the arrow goes because I know the reactants and the products. Do you? If so, place the arrow where it belongs.]

I understand how to balance the rest of the equation, but I just don't understand how to balance the Fe^+2 and Fe^+3 ions on both sides of the equation.

Actually, would it be 3Fe^+2 and 2Fe^+3 for balancing?

To balance the given equation:

MnO4– + H+ + Fe2+ Mn2+ + H2O + Fe3+

Start by examining the atoms on each side of the equation.

On the left side, we have:
1 Mn atom (in MnO4–)
4 O atoms (in MnO4–)
1 H atom (in H+)
1 Fe atom (in Fe2+)

On the right side, we have:
1 Mn atom (in Mn2+)
2 O atoms (in H2O)
1 H atom (in H2O)
1 Fe atom (in Fe3+)

Now, let's attempt to balance the equation:

1. Balance the Mn atoms:
There is 1 Mn atom on each side, so this is already balanced.

2. Balance the O atoms:
On the left side, there are 4 O atoms from MnO4–, while on the right side, there are 2 O atoms from H2O.
To balance the O atoms, we need to add 2 more O atoms on the right side. To do this, we can add a coefficient of 2 in front of H2O:

MnO4– + H+ + Fe2+ -> Mn2+ + 2H2O + Fe3+

3. Balance the H atoms:
On the left side, there is 1 H atom from H+, while on the right side, there are 4 H atoms from 2H2O.
To balance the H atoms, we need to add a coefficient of 4 in front of H+:

MnO4– + 4H+ + Fe2+ -> Mn2+ + 2H2O + Fe3+

4. Balance the Fe atoms:
On the left side, there is 1 Fe atom from Fe2+, while on the right side, there is 1 Fe atom from Fe3+.
To balance the Fe atoms, we can add a coefficient of 1 in front of Fe2+:

MnO4– + 4H+ + Fe2+ -> Mn2+ + 2H2O + Fe3+

The balanced equation is:
MnO4– + 4H+ + Fe2+ -> Mn2+ + 2H2O + Fe3+