F (x) = 3x^2-18x+27

can you solve this?

I can factor it

3x^2 - 18x + 27

= 3 (x^2 - 6x + 9

= 3 (x - 3) ^2

If we equate this to 0 we can solve for x:-

3 (x - 3) ^2 = 0

so x - 3 = 0

and x = 3 (duplicity 2)

What do you mean by "solve this?" Until you set f (x) = to some constant number, you don't have an equation and thus can't expect to find solutions.

Why don't we take 3x^2-18x+27 and set it = to 0, and only then try to solve this equation?

3x^2-18x+27 = 0. Dividing both sides by 3, we get x^2 - 6x + 9 = 0, which can be factored as

(x-3) ^2 = 0. Taking the sqrt of both sides, we get x-3 = 0. Actually, there are 2 roots: 3 and 3. Again, this statement is true only if we set 3x^2-18x+27 = to 0.