-3x^2+12x-9

There is no question here.

-3x^2+12x-9  ?

$$\\-3x^2+12x-9 \quad | \quad : -3 \\ \boxed{x^2-4x+3=0}\\ x^2-4x \text{ } \textcolor[rgb]{1,0,0}{ + 2^2 - 2^2}+3=0\\\\ \left(x-2\right)^2-4+3=0\\\\ \left(x-2\right)^2-1=0\\\\ \left(x-2\right)^2=1\quad | \quad \pm\sqrt{} \\\\ x-2=\pm1\quad |\quad +2\\$$

$$\\x=\pm1+2\\ x_1=1+2=3 \quad\text{and}\quad x_2=-1+2=1\\ \boxed{x_1=3 \quad\text{and}\quad x_2=1}$$