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I used to write out the number of each element below the equations so that I could visualize it better and then look for common factors to balance chemical equations. You could also set up a system of equations with variable coefficients before each molecule in the reaction and balance it that way, whichever is easiest for you:)
I use to have the same problem but to add onto one of the comments I feel like simply guessing and checking to see if your reactants and products are balanced is the best method to take. Simply having your work neatly written out with the multiple attempts you have taken would lead you to the correct equation.
What I like to do is write out the total number of each atom before balancing on each side, then see how the number of atoms changes with different coefficients. If I right down enough of these usually the answer is apparent.
I have tried multiple methods when trying to balance equations, but as some others have already stated. Guess and check is the best way because each balance equation is unique in how it is structured and there isn't one specific method that would work for all of them. It would be the most efficient in my opinion.
Though there isn't really a 'uniform' method, it always helps to start with an element that only appears in only one reactant and only one product. Balance that element first, and start moving to elements that appear multiple times. Some elements like Oxygen can appear multiple times, so it could be difficult to try and balance those right off the bat.
I personally like to write the total number of each atom on both the reactant and product side on the bottom of the given equation so it can be easier for me to visualize it better. Then, I use the guess and check method & use coefficients that will make the equation balanced.
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