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

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

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

We multiply parentheses ..

3(-2x^2-8x)=0

We multiply parentheses

-6x^2-24x=0

a = -6; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·(-6)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*-6}=\frac{48}{-12}
=-4
$