Question

F(x)=3x^2-18x+27can you solve this?

Answer 1

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)

Answer 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.