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

Solution for 4(z+6)(4z+1)=0 equation:

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

We multiply parentheses ..

4(+4z^2+z+24z+6)=0

We multiply parentheses

16z^2+4z+96z+24=0

We add all the numbers together, and all the variables

16z^2+100z+24=0

a = 16; b = 100; c = +24;
Δ = b2-4ac
Δ = 1002-4·16·24
Δ = 8464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8464}=92$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-92}{2*16}=\frac{-192}{32}
=-6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+92}{2*16}=\frac{-8}{32}
=-1/4
$