I have simplified my function down to the above expression, but I'm not sure what to do from here.
How do I factor or solve 2x^2+2x+2 ?
I think you are confusing the terms FACTOR and SOLVE!
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.
If you are looking for 0's of the function, you can use the quadratic formula to find the value of x that equals 0.
If you are just looking for factors of the original expression, you need to factor out the 2 from each term.
2x2 + 2x + 2 Given
2(x2 + x + 1) Factor out a 2
The expression cannot be factored further.