Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.1 - Factoring by Using the Distributive Property - Problem Set 6.1 - Page 243: 63

$x=\{ -1,0 \}$

Factoring out the $GCF= x ,$ the factored form of the given expression, $ x^2+x=0 ,$ is \begin{array}{l}\require{cancel} x(x+1) =0 .\end{array} Equating each factor to zero, wo obtain: \begin{array}{l}\require{cancel} x=0 ,\\\\\text{OR}\\\\ x+1=0 \\\\ x=-1 .\end{array} Hence, the solution set is $ x=\{ -1,0 \} .$