(4z-6)(2-z)=0

Solution for (4z-6)(2-z)=0 equation:

(4z-6)(2-z)=0

We add all the numbers together, and all the variables

(4z-6)(-1z+2)=0

We multiply parentheses ..

(-4z^2+8z+6z-12)=0

We get rid of parentheses

-4z^2+8z+6z-12=0

We add all the numbers together, and all the variables

-4z^2+14z-12=0

a = -4; b = 14; c = -12;
Δ = b2-4ac
Δ = 142-4·(-4)·(-12)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2}{2*-4}=\frac{-16}{-8}
=+2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2}{2*-4}=\frac{-12}{-8}
=1+1/2
$