-4(x+6)-2x(x-9)=-12

Solution for -4(x+6)-2x(x-9)=-12 equation:

-4(x+6)-2x(x-9)=-12

We move all terms to the left:

-4(x+6)-2x(x-9)-(-12)=0

We add all the numbers together, and all the variables

-4(x+6)-2x(x-9)+12=0

We multiply parentheses

-2x^2-4x+18x-24+12=0

We add all the numbers together, and all the variables

-2x^2+14x-12=0

a = -2; b = 14; c = -12;
Δ = b2-4ac
Δ = 142-4·(-2)·(-12)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-10}{2*-2}=\frac{-24}{-4}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10}{2*-2}=\frac{-4}{-4}
=1
$