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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -(2(x+4)), so:

2(x+4)

We multiply parentheses

2x+8

Back to the equation:

-(2x+8)


We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-16=0

a = 1; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·1·(-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{-(0)-8}{2*1}=\frac{-8}{2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*1}=\frac{8}{2}
=4
$