To solve this inequality, we need to find the roots of each factor and then determine the sign of the expression in each interval created by the roots.

The roots of the factors are:
(2x + 5) = 0 → x = -5/2
(4x + 3) = 0 → x = -3/4
(7 - 2x) = 0 → x = 7/2
(x - 3) = 0 → x = 3

Now, we can create the intervals:
-∞ to -5/2
-5/2 to -3/4
-3/4 to 7/2
7/2 to 3
3 to +∞

We will now determine the sign of the expression in each interval:

In the interval -∞ to -5/2:
All factors are negative, so the expression is positive.

In the interval -5/2 to -3/4:
(2x + 5) is positive
(4x + 3) is negative
(7 - 2x) is positive
(x - 3) is negative
The expression is negative in this interval.

In the interval -3/4 to 7/2:
(2x + 5) is positive
(4x + 3) is positive
(7 - 2x) is positive
(x - 3) is negative
The expression is negative in this interval.

In the interval 7/2 to 3:
(2x + 5) is positive
(4x + 3) is positive
(7 - 2x) is negative
(x - 3) is negative
The expression is positive in this interval.

In the interval 3 to +∞:
All factors are positive, so the expression is positive.

Therefore, the solution to the inequality is:
-5/2 < x < -3/4 or 3 < x < 7/2.