X^3 - 3 x^2 + 2 x - 6 > 0

Factor

group them

(x^3-3x^2) + (2x-6) >0

factor

(x^2) (x-3) + (2) (x-3) >0

we see a common factor of (x-3) so undistribute that

(x-3) (x^2+2) >0

set each greater than zero

x-3>0

x>3

x^2+2>0

x^2>-2

true for all real numbers because the square of any real number is always 0 or positive

the answer is all real numbers will work