Given equation:
"Ca"_3("PO"_4)_2+"H"_3"PO"_4"Ca3(PO4)2+H3PO4rarr→"Ca(H"_2"PO"_4)_2"Ca(H2PO4)2
There are three Ca atoms on the left-hand side (LHS), and one on the right-hand side (RHS). Place a coefficient of 33 in front of "Ca(H"_2"PO"_4)_2Ca(H2PO4)2.
"Ca"_3("PO"_4)_2+"H"_3"PO"_4"Ca3(PO4)2+H3PO4rarr→color(teal)3"Ca(H"_2"PO"_4)_2"3Ca(H2PO4)2
Now there are twelve H atoms on the RHS (3xx2xx2)(3×2×2), and three on the LHS. Place a coefficient of 44 in front of "H"_3"PO"_4"H3PO4.
"Ca"_3("PO"_4)_2+color(magenta)4"H"_3"PO"_4"Ca3(PO4)2+4H3PO4rarr→color(teal)3"Ca(H"_2"PO"_4)_2"3Ca(H2PO4)2
Now lets count the number of atoms of each element on each side of the equation.
"LHS:"LHS: "3 Ca atoms"3 Ca atoms, "6 P atoms"6 P atoms, "12 H atoms"12 H atoms, "24 O atoms"24 O atoms
"RHS:"RHS: "3 Ca atoms"3 Ca atoms, "6 P atoms"6 P atoms, "12 H atoms"12 H atoms, "24 O atoms"24 O atoms
Since there are the same number of atoms of each element on both sides of the equation, it is balanced.