Chapter 3 - Polynomial and Rational Functions - Section 3.2 The Real Zeros of a Polynomial Function - 3.2 Assess Your Understanding - Page 224: 65

$x=-\frac{1}{3}$

Step 1. Rewrite the equation as $3x^3-2x^2+8x+3=0$, list possible rational real zeros $\frac{p}{q}: \pm1,\pm3,\pm\frac{1}{3}$ Step 2. Use synthetic division as shown in the figure to find zero(s) $x=-\frac{1}{3}$ Step 3. Use the quotient to find other zeros: $3x^2-3x+9=0$, no real solutions.