Just write it out: All the coefficients in the equation are 1, as this choice gives the same numbers of each of the same kinds of atoms on the right and left sides of the equation, if the formulas given are correct. However, most if not all zinc nitrate has the formula Zn(NO3)2 rather than the one given in the question. that reaction balances as follows:
Zn + 2 AgNO3 = Zn(NO3)2 + 2 Ag.
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