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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-3x^2-12x-(6(-1x-1))=0


We calculate terms in parentheses: -(6(-1x-1)), so:

6(-1x-1)

We multiply parentheses

-6x-6

Back to the equation:

-(-6x-6)


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -3; b = -6; c = +6;
Δ = b2-4ac
Δ = -62-4·(-3)·6
Δ = 108
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{3}}{2*-3}=\frac{6-6\sqrt{3}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{3}}{2*-3}=\frac{6+6\sqrt{3}}{-6}
$