4(x+8)(2x+3)=0

Solution for 4(x+8)(2x+3)=0 equation:

4(x+8)(2x+3)=0

We multiply parentheses ..

4(+2x^2+3x+16x+24)=0

We multiply parentheses

8x^2+12x+64x+96=0

We add all the numbers together, and all the variables

8x^2+76x+96=0

a = 8; b = 76; c = +96;
Δ = b2-4ac
Δ = 762-4·8·96
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-52}{2*8}=\frac{-128}{16}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+52}{2*8}=\frac{-24}{16}
=-1+1/2
$