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

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

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

We move all terms to the left:

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

We use the square of the difference formula

x^2+2x(x-3)-((x+2)(x+3))+9=0

We multiply parentheses

x^2+2x^2-6x-((x+2)(x+3))+9=0

We multiply parentheses ..

x^2+2x^2-((+x^2+3x+2x+6))-6x+9=0


We calculate terms in parentheses: -((+x^2+3x+2x+6)), so:

(+x^2+3x+2x+6)

We get rid of parentheses

x^2+3x+2x+6

We add all the numbers together, and all the variables

x^2+5x+6

Back to the equation:

-(x^2+5x+6)


We add all the numbers together, and all the variables

3x^2-6x-(x^2+5x+6)+9=0

We get rid of parentheses

3x^2-x^2-6x-5x-6+9=0

We add all the numbers together, and all the variables

2x^2-11x+3=0

a = 2; b = -11; c = +3;
Δ = b2-4ac
Δ = -112-4·2·3
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{97}}{2*2}=\frac{11-\sqrt{97}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{97}}{2*2}=\frac{11+\sqrt{97}}{4}
$