quadratics by factoring 2z(5z-2)=-5z+2

Step 1
consider the given quadratic equation,
2z(5z-2)=-5z+2
simplify the quadratic equation as follows,
${\displaystyle 10z^2-4z=-5z+2}$
${\displaystyle 10z^2-4z-5z-2=0}$
${\displaystyle 10z^2+z-z=0}$
Step 2
now factorize the quadratic equation and solve as follows,
${\displaystyle 10z^2+5z-4z-2=0}$
${\displaystyle 5z(2z=1)-1(2z+1)=0}$
${\displaystyle (5z-1)(2z+1)=0}$
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.
${\displaystyle (5z-1)=0\text{or}(2z+1)=0}$
${\displaystyle z=\frac{1}{5}\text{or}z=-\frac{1}{2}}$
so, the value of z is ${\displaystyle \frac{1}{5},-\frac{1}{2}}$