Chapter 3 - Polynomial and Rational Functions - Section 3.2 The Real Zeros of a Polynomial Function - 3.2 Assess Your Understanding - Page 225: 105

$ -8,-4,-\frac{7}{3}$.

Step 1. Use synthetic division or graphing to find zeros of $f(x)=3x^3+16x^2+3x-10$ as $x=-5,-1,\frac{2}{3}$, see graph. Step 2. As $f(x+3)$ can be obtained by shifting $f(x)$ 3 units to the left, the zeros for $f(x+3)$ are $x=-8,-4,-\frac{7}{3}$.