Quadratics by factoring $2z\left(5z-2\right)=-5z+2$
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Asma Vang

$10{z}^{2}-4z=-5z+2$
$1-{z}^{2}-4z+5z-2=0$
$10{z}^{2}+z-2=0$
$10{z}^{2}+5z-4z-2=0$
$5z\left(2z+1\right)-1\left(2z+1\right)=0$
$\left(5z-1\right)\left(2z+1\right)$
Use the principle of zero products which states that if the product of two numbers is zero then at least one of the factors is 0.
$\left(5z-1\right)=0\phantom{\rule{1em}{0ex}}\text{or}\phantom{\rule{1em}{0ex}}\left(2z+1\right)=0$
$z-\frac{1}{5}$ or $z=-\frac{1}{2}$