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

Solution for 6x(x+3)=(2x+12)(x+3) equation:

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

We move all terms to the left:

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

We multiply parentheses

6x^2+18x-((2x+12)(x+3))=0

We multiply parentheses ..

6x^2-((+2x^2+6x+12x+36))+18x=0


We calculate terms in parentheses: -((+2x^2+6x+12x+36)), so:

(+2x^2+6x+12x+36)

We get rid of parentheses

2x^2+6x+12x+36

We add all the numbers together, and all the variables

2x^2+18x+36

Back to the equation:

-(2x^2+18x+36)


We add all the numbers together, and all the variables

6x^2+18x-(2x^2+18x+36)=0

We get rid of parentheses

6x^2-2x^2+18x-18x-36=0

We add all the numbers together, and all the variables

4x^2-36=0

a = 4; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·4·(-36)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*4}=\frac{-24}{8}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*4}=\frac{24}{8}
=3
$