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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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


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

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

We add all the numbers together, and all the variables

(x+1)-2)(x

We get rid of parentheses

x-2)(x+1

Back to the equation:

-(x-2)(x+1)


We multiply parentheses

2x^2-6x+4x-2x-(x-2)(x+1)-12=0

We multiply parentheses ..

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-3x-10=0

a = 1; b = -3; c = -10;
Δ = b2-4ac
Δ = -32-4·1·(-10)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-7}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+7}{2*1}=\frac{10}{2}
=5
$