4(w+3)(-w-7)=0

Solution for 4(w+3)(-w-7)=0 equation:

4(w+3)(-w-7)=0

We add all the numbers together, and all the variables

4(w+3)(-1w-7)=0

We multiply parentheses ..

4(-1w^2-7w-3w-21)=0

We multiply parentheses

-4w^2-28w-12w-84=0

We add all the numbers together, and all the variables

-4w^2-40w-84=0

a = -4; b = -40; c = -84;
Δ = b2-4ac
Δ = -402-4·(-4)·(-84)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-16}{2*-4}=\frac{24}{-8}
=-3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+16}{2*-4}=\frac{56}{-8}
=-7
$