To solve this equation, we will first expand the left side:

(2x-1)³ = (2x-1)(2x-1)(2x-1)
= (4x² - 2x - 2x + 1)(2x-1)
= (4x² - 4x + 1)(2x-1)
= 8x³ - 8x² + 2x² - 2x
= 8x³ - 6x² - 2x

Now, substitute this expression back into the original equation:

8x³ - 6x² - 2x - 4x²(2x-3) = 17
8x³ - 6x² - 2x - 8x² + 12x = 17
8x³ - 14x² + 10x - 17 = 0

This is a cubic equation which is difficult to solve algebraically. One common technique to solve a cubic equation is to use the Rational Root Theorem to try potential rational roots and find one that makes the equation equal to zero.