Celia Horne

2022-02-01

quadratics by factoring

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

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

enguinhispi

Beginner2022-02-02Added 15 answers

Step 1

consider the given quadratic equation,

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,

$10{z}^{2}+5z-4z-2=0$

$5z(2z=1)-1(2z+1)=0$

$(5z-1)(2z+1)=0$

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.

$(5z-1)=0{\textstyle \phantom{\rule{1em}{0ex}}}\text{or}{\textstyle \phantom{\rule{1em}{0ex}}}(2z+1)=0$

$z=\frac{1}{5}{\textstyle \phantom{\rule{1em}{0ex}}}\text{or}{\textstyle \phantom{\rule{1em}{0ex}}}z=-\frac{1}{2}$

so, the value of z is$\frac{1}{5},-\frac{1}{2}$

consider the given quadratic equation,

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

simplify the quadratic equation as follows,

Step 2

now factorize the quadratic equation and solve as follows,

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.

so, the value of z is