-x-x(6x+21)=12

Solution for -x-x(6x+21)=12 equation:

-x-x(6x+21)=12

We move all terms to the left:

-x-x(6x+21)-(12)=0

We add all the numbers together, and all the variables

-1x-x(6x+21)-12=0

We multiply parentheses

-6x^2-1x-21x-12=0

We add all the numbers together, and all the variables

-6x^2-22x-12=0

a = -6; b = -22; c = -12;
Δ = b2-4ac
Δ = -222-4·(-6)·(-12)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-14}{2*-6}=\frac{8}{-12}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+14}{2*-6}=\frac{36}{-12}
=-3
$