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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


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

(x+2)2

We multiply parentheses

2x+4

Back to the equation:

-(2x+4)


We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-1x-10=0

a = 1; b = -1; c = -10;
Δ = b2-4ac
Δ = -12-4·1·(-10)
Δ = 41
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{-(-1)-\sqrt{41}}{2*1}=\frac{1-\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{41}}{2*1}=\frac{1+\sqrt{41}}{2}
$