4(8z+4)(5z+10)=0

Solution for 4(8z+4)(5z+10)=0 equation:

4(8z+4)(5z+10)=0

We multiply parentheses ..

4(+40z^2+80z+20z+40)=0

We multiply parentheses

160z^2+320z+80z+160=0

We add all the numbers together, and all the variables

160z^2+400z+160=0

a = 160; b = 400; c = +160;
Δ = b2-4ac
Δ = 4002-4·160·160
Δ = 57600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57600}=240$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-240}{2*160}=\frac{-640}{320}
=-2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+240}{2*160}=\frac{-160}{320}
=-1/2
$