Well, the answer is that there is no easy way to balance chemical equations. Some ways are easier than others but they all require some guesstimation. The best formula I've found to balance equations is to do the steps in the following order.
-Unchanged polyatomic ions (Nitrates, sulfates, etc.)
-then either Hydrogen or Oxygen depending on which one works better
After that, just go back through and double check. Sometimes you have to play with it a little bit. Let me give you an example to see if it helps clear things up and make them any easier.
Ca3P2 + H2O --> Ca (OH)2 + PH3
So balance the calcium first. There's three on the left side. So we'll add a 3 to the front of of Ca(OH)2. Remember you can only add numbers to the front of the substances, not the subscripts. So we get:
Ca3P2+ H2O --> 3Ca (OH)2 + PH3
Now, we balance the Phosphorus. There's 2 on the left, but only one on the right. It needs to be multiplied by 2. So we put the 2 in front of PH3.
Ca3P2 + H2O --> 3Ca (OH)2 + 2PH3
Now the Calcium (metal) and Phosphorus (non-metal) are both balanced. Let's work on the Hydrogen. We have 2 on the left, and 12 on the right. So we need to add a 6 in front of the H2O on the left. Doing that we get the following:
Ca3P2 + 6H2O --> 3Ca (OH) 2 + 2PH3
Now everything is balanced except the Oxygen. We have 6 on the left and coincidentally we have 6 on the right. It balanced itself by balancing the water.
If you work them this way, it will save you from most problems. Hope this helped.