Chapter 5 - Polynomials and Factoring - 5.7 Solving Quadratic Equations by Factoring - 5.7 Exercise Set - Page 351: 18

$x=\left\{ 0,\dfrac{5}{4} \right\}$

Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $ 10n(4n-5)=0 ,$ is \begin{array}{l}\require{cancel} 10n=0 \\\\ n=\dfrac{0}{10} \\\\ n=0 ,\\\\\text{OR}\\\\ 4n-5=0 \\\\ 4n=5 \\\\ n=\dfrac{5}{4} .\end{array} Hence, $ x=\left\{ 0,\dfrac{5}{4} \right\} .$