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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

x(2x+3)

We multiply parentheses

2x^2+3x

Back to the equation:

-(2x^2+3x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = 3; c = +9;
Δ = b2-4ac
Δ = 32-4·(-2)·9
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*-2}=\frac{-12}{-4}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*-2}=\frac{6}{-4}
=-1+1/2
$