Celia Horne

2022-02-01

2z(5z-2)=-5z+2

enguinhispi

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

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