(-3*x-9)*(-4*x-7)+4*(-3*x-9)=0

Solution for (-3*x-9)*(-4*x-7)+4*(-3*x-9)=0 equation:

(-3x-9)(-4x-7)+4(-3x-9)=0

We multiply parentheses

(-3x-9)(-4x-7)-12x-36=0

We multiply parentheses ..

(+12x^2+21x+36x+63)-12x-36=0

We get rid of parentheses

12x^2+21x+36x-12x+63-36=0

We add all the numbers together, and all the variables

12x^2+45x+27=0

a = 12; b = 45; c = +27;
Δ = b2-4ac
Δ = 452-4·12·27
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-27}{2*12}=\frac{-72}{24}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+27}{2*12}=\frac{-18}{24}
=-3/4
$