2x+2x(x+2)=2x(5-x)

Solution for 2x+2x(x+2)=2x(5-x) equation:

2x+2x(x+2)=2x(5-x)

We move all terms to the left:

2x+2x(x+2)-(2x(5-x))=0

We add all the numbers together, and all the variables

2x+2x(x+2)-(2x(-1x+5))=0

We multiply parentheses

2x^2+2x+4x-(2x(-1x+5))=0


We calculate terms in parentheses: -(2x(-1x+5)), so:

2x(-1x+5)

We multiply parentheses

-2x^2+10x

Back to the equation:

-(-2x^2+10x)


We add all the numbers together, and all the variables

2x^2-(-2x^2+10x)+6x=0

We get rid of parentheses

2x^2+2x^2-10x+6x=0

We add all the numbers together, and all the variables

4x^2-4x=0

a = 4; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·4·0
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{-(-4)-4}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*4}=\frac{8}{8}
=1
$