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

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

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

We multiply parentheses ..

4(+2x^2-4x+2x-4)=0

We multiply parentheses

8x^2-16x+8x-16=0

We add all the numbers together, and all the variables

8x^2-8x-16=0

a = 8; b = -8; c = -16;
Δ = b2-4ac
Δ = -82-4·8·(-16)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-24}{2*8}=\frac{-16}{16}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+24}{2*8}=\frac{32}{16}
=2
$