There's a trick to doing this sort of "number" word problem. To learn how to use it, try here
Once you've studied the above:
i) Pick a variable for the first of the three numbers.
ii) Use the relationship between "consecutive even [or odd] integers" to create an expression, in terms of the variable in (i), for the second of the three numbers.
iii) Following the same reasoning as in (ii), create an expression for the third of the three numbers.
Plug the variable in (i) and the expression in (iii) into the form of the equation you have already developed. Then solve the result for the value of the variable, and then back-solve for the three numbers.
If you get stuck, please reply showing your steps and reasoning, starting from the variable you picked and what it stands for. Thank you!