Simplifying
3q2 + -12q + 12

Reorder the terms:
12 + -12q + 3q2

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -4q + q2)

Factor a trinomial.
3((2 + -1q)(2 + -1q))

Final result:
3(2 + -1q)(2 + -1q)