Let's rewrite and factorise the inequality
#x^3-4x^2-3x<=0#
#x(x^2-4x-3))<=0#
We calculate the roots of the equation #x^2-4x-3=0#
#Delta=(-4)^2-4*1*(-3)=16+12=28#
#x_1=(4+sqrt28)/2=(4+2sqrt7)/2=2+sqrt7#
#x_2=(4-sqrt28)/2=(4-2sqrt7)/2=2-sqrt7#
Let #f(x)=x(x-(2+sqrt7))(x-(2-sqrt7))#
Now, we build the sign chart
#color(white)(aaaa)##x##color(white)(aaaaaaa)##-oo##color(white)(aaaa)##2-sqrt7##color(white)(aaaa)##0##color(white)(aaaa)##2+sqrt7##color(white)(aaaa)##+oo#
#color(white)(aaaa)##x-x_2##color(white)(aaaaaaa)##-##color(white)(aaaaaaa)##+##color(white)(aaaa)##+##color(white)(aaaaaaa)##+#
#color(white)(aaaa)##x-x_1##color(white)(aaaaaaa)##-##color(white)(aaaaaaa)##-##color(white)(aaaa)##-##color(white)(aaaaaaa)##+#
#color(white)(aaaa)##x##color(white)(aaaaaaaaaaaa)##-##color(white)(aaaaaaa)##-##color(white)(aaaa)##+##color(white)(aaaaaaa)##+#
#color(white)(aaaa)##f(x)##color(white)(aaaaaaaaa)##-##color(white)(aaaaaaa)##+##color(white)(aaaa)##-##color(white)(aaaaaaa)##+#
Therefore,
#f(x)<=0# when #x in ]-oo,2-sqrt7]uu [0,2+sqrt7]#