#### Answer

The only possible solutions for this equation are: 0, 1, and 2

#### Work Step by Step

Step 1) Consecutive integers can be represented by (N), (N+1), and (N+2). We set up our equation exactly as the problem describes with the 3rd integer (N+2) being 2x the sum of the 1st and 2nd integers (N and N +1).
Step 2) Using PEMDAS, do what is in parenthesis first.
Step 3) Using distributive property, multiply 2 through the right side.
Step 4) Combine like terms by subtracting 1N from each side and subtracting 2 from each side.
Step 5) Solve for N by dividing each side by 3. Now that we have N, we can plug into our integer setup (see step 1) in order to solve for all three integers.