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+24x+16=0

a = 8; b = 24; c = +16;
Δ = b2-4ac
Δ = 242-4·8·16
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8}{2*8}=\frac{-32}{16}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8}{2*8}=\frac{-16}{16}
=-1
$