This sounds like a homework problem but nevertheless.
Breaking it down into operands and operators is a good start. But you'll need to keep a good record of their position in the equation.
Next step would be iterate through your BOMDAS to do each step separately.
So search through your operands if you see a bracket do that part of the equation first, however note with brackets this will need to start the BOMDAS evaluation all over again. So maybe implement it in a recursive function could be powerful.
Next search through for a multiplication. If you find one multiple the two operatands on either side. This will result in a new operand between the existing two operators.
Continue iterating through each element of the BOMDAS ensuring when performing an operation the new operand is put in place of the existing two operands and operator.