To solve this equation, we will first expand both sides of the equation:

Left side: (5x+1)(2x-3)
= 5x(2x) + 5x(-3) + 1(2x) + 1(-3)
= 10x^2 - 15x + 2x - 3
= 10x^2 - 13x - 3

Right side: (10x-3)(x+1)
= 10x(x) + 10x(1) - 3(x) - 3(1)
= 10x^2 + 10x - 3x - 3
= 10x^2 + 7x - 3

Therefore, the equation becomes:
10x^2 - 13x - 3 = 10x^2 + 7x - 3

Simplify by canceling out the common terms:
-13x = 7x

Add 13x to both sides:
-13x + 13x = 7x + 13x
0 = 20x

Rearranging:
x = 0

Therefore, the solution to the equation (5x+1)(2x-3) = (10x-3)(x+1) is x = 0.