The order that always works

1. GCF first — take out what every term shares.
2. Special patterns — $a^2 - b^2 = (a + b)(a - b)$, $a^2 \pm 2ab + b^2 = (a \pm b)^2$.
3. $x^2 + bx + c$ — two numbers with product $c$ and sum $b$.
4. $ax^2 + bx + c$ — the ac-method: product $ac$, sum $b$, split the middle term, group.