Make your leading term positive. This is the term with the highest exponent, usually the first one on the left. In the example -3x^2 + 6x - 9 , the leading term is -3x^2. Make the leading term positive by rewriting the trinomial as 3(x^2 + 2x - 3). This removes the negative factor - 3 and simplifies the trinomial because 3 is the greatest common factor among 3, 6 and 9.
Factor out the simplified trinomial into two binomials, algebraic expressions with two terms. Leaving the negative factor out, write two sets of parentheses, factoring out the leading term. For example, x^2 would be factored out (x )(x ). Find a pair of factors whose product is 3 and sum is 2. The only possible factor pair is 1 and 3. Add them to your binomial expression: (x 3)(x 1).
Add signs to make your binomial expression equal your trinomial expression. For example, (x + 3)(x - 1). Multiply the binomial expressions to make sure your signs are correct. You may need to change one or both signs to make your binomials equal your trinomial expression. (x + 3)(x - 1) = x^2 + 2x - 3, so the signs are correct for these binomials.
Write your final answer including your factored-out negative term, - 3, as well as your factored-out binomial expressions. The final answer for this example is -3x^2 + 6x - 9 = -3(x + 3)(x - 1).