Since hydrogen and oxygen are present in only one compound on the left side, the next step is to assign a coefficient that balances these atoms. There are six atoms each of oxygen and hydrogen on the right side of the reaction.
The potassium can now be balanced. Six atoms of potassium can be represented on the right by multiplying the coefficient of either of the two compounds containing potassium by 5. Since it has been observed that adjustments to chlorine on the left side can be made without affecting any other atom, it is reasonable to multiply the coefficient of potassium chloride by 5.
Now all that remains to be balanced is the chlorine. There are six atoms of chlorine on the right side of the equation, so a coefficient of three for chlorine balances the overall equation.
