Final answer:
The roots of the given cubic equation are x = 3, x = 1/8, and x = 5/8.
Step-by-step explanation:
The given equation 64x³ - 144x² + 92x - 15 = 0 is a cubic equation. To find the roots, we can use various methods such as synthetic division or factoring. In this case, let's use synthetic division to simplify the equation:
64x^3 - 144x^2 + 92x - 15 = 0
(x - 3)(8x - 1)(8x - 5) = 0
The roots of the equation are x = 3, x = 1/8, and x = 5/8.