4(w-6)(-w-9)=0

Solution for 4(w-6)(-w-9)=0 equation:

4(w-6)(-w-9)=0

We add all the numbers together, and all the variables

4(w-6)(-1w-9)=0

We multiply parentheses ..

4(-1w^2-9w+6w+54)=0

We multiply parentheses

-4w^2-36w+24w+216=0

We add all the numbers together, and all the variables

-4w^2-12w+216=0

a = -4; b = -12; c = +216;
Δ = b2-4ac
Δ = -122-4·(-4)·216
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-60}{2*-4}=\frac{-48}{-8}
=+6
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+60}{2*-4}=\frac{72}{-8}
=-9
$