-2x(-3x-4)=4x(4+x)

Solution for -2x(-3x-4)=4x(4+x) equation:

-2x(-3x-4)=4x(4+x)

We move all terms to the left:

-2x(-3x-4)-(4x(4+x))=0

We add all the numbers together, and all the variables

-2x(-3x-4)-(4x(x+4))=0

We multiply parentheses

6x^2+8x-(4x(x+4))=0


We calculate terms in parentheses: -(4x(x+4)), so:

4x(x+4)

We multiply parentheses

4x^2+16x

Back to the equation:

-(4x^2+16x)


We get rid of parentheses

6x^2-4x^2+8x-16x=0

We add all the numbers together, and all the variables

2x^2-8x=0

a = 2; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·2·0
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{-(-8)-8}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*2}=\frac{16}{4}
=4
$