-4x(6+3x)=0

Solution for -4x(6+3x)=0 equation:

-4x(6+3x)=0

We add all the numbers together, and all the variables

-4x(3x+6)=0

We multiply parentheses

-12x^2-24x=0

a = -12; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·(-12)·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*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*-12}=\frac{48}{-24}
=-2
$