6(x+4)+3x(x+4)=0

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

6(x+4)+3x(x+4)=0

We multiply parentheses

3x^2+6x+12x+24=0

We add all the numbers together, and all the variables

3x^2+18x+24=0

a = 3; b = 18; c = +24;
Δ = b2-4ac
Δ = 182-4·3·24
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6}{2*3}=\frac{-24}{6}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6}{2*3}=\frac{-12}{6}
=-2
$