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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We multiply parentheses ..

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


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

x(x+1)

We multiply parentheses

x^2+x

Back to the equation:

-(x^2+x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2+7x+6=0

a = 1; b = 7; c = +6;
Δ = b2-4ac
Δ = 72-4·1·6
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{-(7)-5}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+5}{2*1}=\frac{-2}{2}
=-1
$