## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$z=\left\{ 0,\dfrac{4}{3} \right\}$
Using the properties of equality, the given expression, $15z^2+7=20z+7 ,$ is equivalent to \begin{array}{l}\require{cancel} 15z^2-20z+7-7=0 \\\\ 15z^2-20z=0 .\end{array} Factoring the above equation, $15z^2-20z=0 ,$ results to \begin{array}{l}\require{cancel} 5z(3z-4) .\end{array} Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $5z(3z-4) ,$ are \begin{array}{l}\require{cancel} 5z=0 \\\\ z=\dfrac{0}{5} \\\\ z=0 ,\\\\\text{OR}\\\\ 3z-4=0 \\\\ 3z=4 \\\\ z=\dfrac{4}{3} .\end{array} Hence, $z=\left\{ 0,\dfrac{4}{3} \right\} .$