The inequality is
#x^3-2x^2<5x-6#
#x^3-2x^2-5x+6<0#
Let #f(x)=x^3-2x^2-5x+6#
Then,
#f(1)=1-2-5-6=0#
#(x-1)# is a factor
Perform a long division
#f(x)=(x-1)(x^2-x-6)=(x-1)(x+2)(x-3)#
Now, build a sign chart
#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##-2##color(white)(aaaa)##1##color(white)(aaaaa)##3##color(white)(aaaa)##+oo#
#color(white)(aaaa)##x+2##color(white)(aaaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##+##color(white)(aaaa)##+#
#color(white)(aaaa)##x-1##color(white)(aaaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##+#
#color(white)(aaaa)##x-3##color(white)(aaaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##+#
#color(white)(aaaa)##f(x)##color(white)(aaaaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##-##color(white)(aaaa)##+#
Therefore,
#f(x)<0# when #x in (-oo,-2)uu(1,3)#
graph{x^3-2x^2-5x+6 [-14.36, 14.12, -5.01, 9.23]}