(2x+3)(x-2)+2x=-2(x+1)-2(x+2)

Solution for (2x+3)(x-2)+2x=-2(x+1)-2(x+2) equation:

(2x+3)(x-2)+2x=-2(x+1)-2(x+2)

We move all terms to the left:

(2x+3)(x-2)+2x-(-2(x+1)-2(x+2))=0

We add all the numbers together, and all the variables

2x+(2x+3)(x-2)-(-2(x+1)-2(x+2))=0

We multiply parentheses ..

(+2x^2-4x+3x-6)+2x-(-2(x+1)-2(x+2))=0


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

-2(x+1)-2(x+2)

We multiply parentheses

-2x-2x-2-4

We add all the numbers together, and all the variables

-4x-6

Back to the equation:

-(-4x-6)


We get rid of parentheses

2x^2-4x+3x+2x+4x-6+6=0

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