Intermediate Algebra: Connecting Concepts through Application

$\color{blue}{\left\{0 , \dfrac{26}{47}\right\}}$
Factor out $4.7x$ to obtain: \begin{align*} 4.7x\left(x-\frac{2.6}{4.7}\right)&=0\\\\ 4.7x\left(x-\frac{26}{47}\right)&=0\\\\ \end{align*} Use the Zero-Product Property by equating each factor to zero. Then, solve each equation to obtain: \begin{align*} 4.7x&=0 &\text{or}& &x-\frac{26}{47}&=0\\\\ x&=0 &\text{or}& &x=\frac{26}{47}\\\\ \end{align*} Therefore, the solution set is $\color{blue}{\left\{0 , \dfrac{26}{47}\right\}}$.