(2+x)(3+2x)=9x+6

Solution for (2+x)(3+2x)=9x+6 equation:

(2+x)(3+2x)=9x+6

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply parentheses ..

(+2x^2+3x+4x+6)-9x-6=0

We get rid of parentheses

2x^2+3x+4x-9x+6-6=0

We add all the numbers together, and all the variables

2x^2-2x=0

a = 2; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·2·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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