Verified answer

(2x+1)(x+3)-(2x+1)(5x+1)<0

(2x+1)(x+3-5x-1)<0

(2x+1)(-4x+2)<0

(2x+1)<0 ou (-4x+2)<0

2x<-1      ou  -4x<-2

x<-1/2     ou   x>1/2

Ainsi, (2x+1)(x+3)-(2x+1)(5x+1)<0 quand x∈]-∞;-1/2[∪]1/2;+∞[