3(z+7)(-z+8)=0

Solution for 3(z+7)(-z+8)=0 equation:

3(z+7)(-z+8)=0

We add all the numbers together, and all the variables

3(z+7)(-1z+8)=0

We multiply parentheses ..

3(-1z^2+8z-7z+56)=0

We multiply parentheses

-3z^2+24z-21z+168=0

We add all the numbers together, and all the variables

-3z^2+3z+168=0

a = -3; b = 3; c = +168;
Δ = b2-4ac
Δ = 32-4·(-3)·168
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-45}{2*-3}=\frac{-48}{-6}
=+8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+45}{2*-3}=\frac{42}{-6}
=-7
$