To solve for x in the given equation, we need to first simplify both sides of the equation and then find a common denominator to combine like terms.

Starting with the left side of the equation:

3x/(2x+5) - 4x/(2x-5)

To combine the fractions, we need to find a common denominator, which will be (2x+5)(2x-5):

(3x(2x-5) - 4x(2x+5))/((2x+5)(2x-5))

Expanding and simplifying the numerator:

(6x^2 - 15x - 8x^2 - 20x)/((2x+5)(2x-5))

(-2x^2 - 35x)/((2x+5)(2x-5)) = (-x(2x + 35))/((2x+5)(2x-5))

Moving on to the right side of the equation:

28 - 53x/(4x^2 - 25)

We can factor the denominator to simplify the fraction:

4x^2 - 25 = (2x - 5)(2x + 5)

Combining the terms on the right side:

28 - 53x/((2x - 5)(2x + 5))

Now we have the equation in the form:

(-x(2x + 35))/((2x+5)(2x-5)) = 28 - 53x/((2x - 5)(2x + 5))

To solve for x, we can now cross multiply to eliminate the denominators:

(-x(2x + 35)) = (28 - 53x)(2x + 5)

Expanding both sides and simplifying the equation will lead to a quadratic equation that can be solved to find the value(s) of x.