(6-z)(2z+7)=0

Solution for (6-z)(2z+7)=0 equation:

(6-z)(2z+7)=0

We add all the numbers together, and all the variables

(-1z+6)(2z+7)=0

We multiply parentheses ..

(-2z^2-7z+12z+42)=0

We get rid of parentheses

-2z^2-7z+12z+42=0

We add all the numbers together, and all the variables

-2z^2+5z+42=0

a = -2; b = 5; c = +42;
Δ = b2-4ac
Δ = 52-4·(-2)·42
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-19}{2*-2}=\frac{-24}{-4}
=+6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+19}{2*-2}=\frac{14}{-4}
=-3+1/2
$