(3-z)(5z+7)=0

Solution for (3-z)(5z+7)=0 equation:

(3-z)(5z+7)=0

We add all the numbers together, and all the variables

(-1z+3)(5z+7)=0

We multiply parentheses ..

(-5z^2-7z+15z+21)=0

We get rid of parentheses

-5z^2-7z+15z+21=0

We add all the numbers together, and all the variables

-5z^2+8z+21=0

a = -5; b = 8; c = +21;
Δ = b2-4ac
Δ = 82-4·(-5)·21
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-22}{2*-5}=\frac{-30}{-10}
=+3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+22}{2*-5}=\frac{14}{-10}
=-1+2/5
$