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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

(x+2)6

We multiply parentheses

6x+12

Back to the equation:

-(6x+12)


We get rid of parentheses

3x^2+6x-6x-12=0

We add all the numbers together, and all the variables

3x^2-12=0

a = 3; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·3·(-12)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*3}=\frac{-12}{6}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*3}=\frac{12}{6}
=2
$