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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-4x^2-4x-8x=0

We add all the numbers together, and all the variables

-4x^2-12x=0

a = -4; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-4)·0
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{-(-12)-12}{2*-4}=\frac{0}{-8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-4}=\frac{24}{-8}
=-3
$