Chapter 5 Polynomials and Polynomial Functions - 5.4 Factor and Solve Polynomial Equations - 5.4 Exercises - Problem Solving - Page 359: 64c

$x=\frac{16}{3}$

Calculate $y^3+y^2$ for $y=1,2,...,10$ Solve $3x^3+2x^2=512\\ \Leftrightarrow (\frac{3x}{2})^3+(\frac{3x}{2})^2=\frac{512\times9}{8}=64\times9=576$ Search for values of $12$ in the table. It matches $y=8$. Hence, $\frac{3x}{2}=8 \rightarrow x=\frac{16}{3}$