4(2x-1)(3x+6)=0

Solution for 4(2x-1)(3x+6)=0 equation:

4(2x-1)(3x+6)=0

We multiply parentheses ..

4(+6x^2+12x-3x-6)=0

We multiply parentheses

24x^2+48x-12x-24=0

We add all the numbers together, and all the variables

24x^2+36x-24=0

a = 24; b = 36; c = -24;
Δ = b2-4ac
Δ = 362-4·24·(-24)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-60}{2*24}=\frac{-96}{48}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+60}{2*24}=\frac{24}{48}
=1/2
$