(3x+6)(x+1)=(3x+6)(2x-4)

Solution for (3x+6)(x+1)=(3x+6)(2x-4) equation:

(3x+6)(x+1)=(3x+6)(2x-4)

We move all terms to the left:

(3x+6)(x+1)-((3x+6)(2x-4))=0

We multiply parentheses ..

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


We calculate terms in parentheses: -((3x+6)(2x-4)), so:

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

We multiply parentheses ..

(+6x^2-12x+12x-24)

We get rid of parentheses

6x^2-12x+12x-24

We add all the numbers together, and all the variables

6x^2-24

Back to the equation:

-(6x^2-24)


We get rid of parentheses

3x^2-6x^2+3x+6x+6+24=0

We add all the numbers together, and all the variables

-3x^2+9x+30=0

a = -3; b = 9; c = +30;
Δ = b2-4ac
Δ = 92-4·(-3)·30
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-21}{2*-3}=\frac{-30}{-6}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+21}{2*-3}=\frac{12}{-6}
=-2
$