4(4z+7)(z-6)=0

Solution for 4(4z+7)(z-6)=0 equation:

4(4z+7)(z-6)=0

We multiply parentheses ..

4(+4z^2-24z+7z-42)=0

We multiply parentheses

16z^2-96z+28z-168=0

We add all the numbers together, and all the variables

16z^2-68z-168=0

a = 16; b = -68; c = -168;
Δ = b2-4ac
Δ = -682-4·16·(-168)
Δ = 15376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15376}=124$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-124}{2*16}=\frac{-56}{32}
=-1+3/4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+124}{2*16}=\frac{192}{32}
=6
$