When you studied Chemistry, balancing equation was about integer valence(s).
This is solving Diophantine. Chemical balance may be wrt non-integer valence(s).
No direct solver(s) will do. The system must be put in form of matrix,
then create the PseudoInverse that will solve.

Jean

Solve Diophantine Chemical Balance.sm (47 KiB) downloaded 69 time(s).

Matrix PseudoInverse.sm (111 KiB) downloaded 67 time(s).