Solve the inequality: (x+3)(x−4)<−12

0<x<1

Step-by-step explanation:

(x+3)(x−4)<−12

FOIL

x^2 -4x+3x -12 <-12

x^2 -x -12 <-12

Add 12 to each side

x^2 -x -12+12 <-12+12

x^2 -x <0

Factor out an x

x(x-1) <0

Using the zero product property

x(x-1) =0

x=0  x-1=0

x=0  x=1

Check the ranges

x<0

x(x-1) <0        

- * - >0

False

0<x<1

x(x-1) <0        

+ * - <0

True

x>1

x(x-1) <0        

+ * + >0

False