balanced redox equation

Firstly, write the half equation of the reduction of the oxidizing agent (acidified KMnO4) and that of the oxidation of the reducing agent (H2O2).

The half equation of the reduction of acidified KMnO4:
MnO4^-(aq) + 8H^+(aq) + 5e^- → Mn^2+(aq) + 4H2O(l) ... (1)

The half equation of the oxidation of H2O2 in an acidic medium:
H2O2(aq) → 2H^+(aq) + O2(g) + 2e^- ... (2)

2x(1) + 5x(2), then cancel 10e- and 10H^+(aq) on both sides. The overall equation is:
2MnO4^-(aq) + 6H^+(aq) + 5H2O2(aq) → 2Mn^2+(aq) + 8H2O(l) + 5O2(g)