Let's factor:
Taking -3 common:
[tex]\begin{gathered} -3x^2-6x+45 \\ -3(x^2+2x-15) \end{gathered}[/tex]Now, think of two numbers, when multiplied gives you -15 and when added gives you +2.
It's +5 and -3
So now we can factor:
[tex]\begin{gathered} -3(x^2+5x-3x-15) \\ -3(x(x+5)-3(x+5)) \\ -3(x+5)(x-3) \end{gathered}[/tex]