Step 1 :Set the function equal to zero: \(8x^{3}-42x^{2}+67x-30 = 0\).
Step 2 :This is a cubic equation, so it might have up to three real roots.
Step 3 :The roots of the function are the values of x for which the function equals zero.
Step 4 :Calculate the roots of the function.
Step 5 :The roots of the function are 2.5, 2, and 0.75.
Step 6 :Final Answer: The zeros of the function are \(\boxed{2.5, 2, 0.75}\).