-2x(x+3)+2x=(x+6)-6

Solution for -2x(x+3)+2x=(x+6)-6 equation:

-2x(x+3)+2x=(x+6)-6

We move all terms to the left:

-2x(x+3)+2x-((x+6)-6)=0

We add all the numbers together, and all the variables

2x-2x(x+3)-((x+6)-6)=0

We multiply parentheses

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


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

(x+6)-6

We get rid of parentheses

x+6-6

We add all the numbers together, and all the variables

x

Back to the equation:

-(x)


We add all the numbers together, and all the variables

-2x^2-5x=0

a = -2; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-2)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-2}=\frac{0}{-4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-2}=\frac{10}{-4}
=-2+1/2
$