2x(x+2)=(x-6)(x+2)

Solution for 2x(x+2)=(x-6)(x+2) equation:

2x(x+2)=(x-6)(x+2)

We move all terms to the left:

2x(x+2)-((x-6)(x+2))=0

We multiply parentheses

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

We multiply parentheses ..

2x^2-((+x^2+2x-6x-12))+4x=0


We calculate terms in parentheses: -((+x^2+2x-6x-12)), so:

(+x^2+2x-6x-12)

We get rid of parentheses

x^2+2x-6x-12

We add all the numbers together, and all the variables

x^2-4x-12

Back to the equation:

-(x^2-4x-12)


We add all the numbers together, and all the variables

2x^2+4x-(x^2-4x-12)=0

We get rid of parentheses

2x^2-x^2+4x+4x+12=0

We add all the numbers together, and all the variables

x^2+8x+12=0

a = 1; b = 8; c = +12;
Δ = b2-4ac
Δ = 82-4·1·12
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4}{2*1}=\frac{-4}{2}
=-2
$