(3-z)(4z+6)=0

Solution for (3-z)(4z+6)=0 equation:

(3-z)(4z+6)=0

We add all the numbers together, and all the variables

(-1z+3)(4z+6)=0

We multiply parentheses ..

(-4z^2-6z+12z+18)=0

We get rid of parentheses

-4z^2-6z+12z+18=0

We add all the numbers together, and all the variables

-4z^2+6z+18=0

a = -4; b = 6; c = +18;
Δ = b2-4ac
Δ = 62-4·(-4)·18
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-18}{2*-4}=\frac{-24}{-8}
=+3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+18}{2*-4}=\frac{12}{-8}
=-1+1/2
$