In order to solve this inequality we need to graph:

y = (×+3)(×-4) - 7

and see for what values of 'x' the graph for 'y' goes below the x-axis:

Click here to see the graph

 

We will find the zeros by solving:

(×+3)(×-4) - 7 = 0

........

Click here to see the step by step solution for x

........

x1 = 4.89 approximately

x2 = -3.89 approximately

So, the solution for the inequality '(×+3)(×-4)<7' is the interval (-3.89, 4.89).