-4(2x-12)(-3x-21)=0

Solution for -4(2x-12)(-3x-21)=0 equation:

-4(2x-12)(-3x-21)=0

We multiply parentheses ..

-4(-6x^2-42x+36x+252)=0

We multiply parentheses

24x^2+168x-144x-1008=0

We add all the numbers together, and all the variables

24x^2+24x-1008=0

a = 24; b = 24; c = -1008;
Δ = b2-4ac
Δ = 242-4·24·(-1008)
Δ = 97344
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{97344}=312$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-312}{2*24}=\frac{-336}{48}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+312}{2*24}=\frac{288}{48}
=6
$