Find all real numbers \(x\) so that the product \((x + i)((x + 1) + i)((x + 2) + i)\) is pure imaginary. Enter all the solutions, separated by commas.

You might just want to try to expand how it is right now.

If you expand it, the real part is x^3 + 2x^2 - 3x, which factors as x(x + 3)(x - 1). So the solutions are 0, -3, and 1.

actually, the answers are 1, -1, and -3. I solved it!!! I did use the expanding advice