3(2x+4)=2x(3x+6)

Solution for 3(2x+4)=2x(3x+6) equation:

3(2x+4)=2x(3x+6)

We move all terms to the left:

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

We multiply parentheses

6x-(2x(3x+6))+12=0


We calculate terms in parentheses: -(2x(3x+6)), so:

2x(3x+6)

We multiply parentheses

6x^2+12x

Back to the equation:

-(6x^2+12x)


We get rid of parentheses

-6x^2+6x-12x+12=0

We add all the numbers together, and all the variables

-6x^2-6x+12=0

a = -6; b = -6; c = +12;
Δ = b2-4ac
Δ = -62-4·(-6)·12
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-18}{2*-6}=\frac{-12}{-12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+18}{2*-6}=\frac{24}{-12}
=-2
$