-6x*(x+4)=-42

Solution for -6x*(x+4)=-42 equation:

-6x(x+4)=-42

We move all terms to the left:

-6x(x+4)-(-42)=0

We add all the numbers together, and all the variables

-6x(x+4)+42=0

We multiply parentheses

-6x^2-24x+42=0

a = -6; b = -24; c = +42;
Δ = b2-4ac
Δ = -242-4·(-6)·42
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{11}}{2*-6}=\frac{24-12\sqrt{11}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{11}}{2*-6}=\frac{24+12\sqrt{11}}{-12}
$