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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

x+2(x+3)

We multiply parentheses

x+2x+6

We add all the numbers together, and all the variables

3x+6

Back to the equation:

-(3x+6)


We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2+3x-6=0

a = 3; b = 3; c = -6;
Δ = b2-4ac
Δ = 32-4·3·(-6)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-9}{2*3}=\frac{-12}{6}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*3}=\frac{6}{6}
=1
$