I have simplified my function down to the above expression, but I'm not sure what to do from here.

I think you are confusing the terms FACTOR and SOLVE!

The expression

2x^2+2x+2 is already SIMPLIFIED! You could find the FACTORS of the terms of this POLYNOMIAL. In this case the FACTORS common to each term is "2". This leads to new expression 2(x^2+x+ 1). Understanding the concepts (and vocabulary) are just important (if not more) than manipulation of the symbol and numbers.