Introduction:
To determine the value of x such that the given expressions form an arithmetic progression (AP), we need to find a common difference between the terms. An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is constant.

Given expressions:
The given expressions are (7x-5)(5x-2) and (-4x+15).

Expanding the first expression:
To simplify the first expression, we will expand the given quadratic expression using the FOIL method:
(7x-5)(5x-2) = 35x^2 - 14x - 25x + 10 = 35x^2 - 39x + 10

Determining the common difference:
To form an arithmetic progression, the common difference between the terms should be the same for both the first and second expressions.

Comparing coefficients:
We will compare the coefficients of x in the expanded quadratic expression (35x^2 - 39x + 10) and the linear expression (-4x + 15).

Coefficient of x:
The coefficient of x in the quadratic expression is -39, and in the linear expression is -4.

Equating the coefficients:
To find the value of x that satisfies the condition, we equate the coefficients of x in both expressions and solve the equation:
-39 = -4

Solving the equation:
Simplifying the equation, we get:
-39 + 4 = 0
-35 = 0

Conclusion:
Since the equation -35 = 0 is not true for any value of x, there is no value of x that will make the given expressions form an arithmetic progression.