x(16-x)-4(16-x)=0

Solution for x(16-x)-4(16-x)=0 equation:

x(16-x)-4(16-x)=0

We add all the numbers together, and all the variables

x(-1x+16)-4(-1x+16)=0

We multiply parentheses

-1x^2+16x+4x-64=0

We add all the numbers together, and all the variables

-1x^2+20x-64=0

a = -1; b = 20; c = -64;
Δ = b2-4ac
Δ = 202-4·(-1)·(-64)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-12}{2*-1}=\frac{-32}{-2}
=+16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+12}{2*-1}=\frac{-8}{-2}
=+4
$