6x(x+3)-9x(x+3)=0

Solution for 6x(x+3)-9x(x+3)=0 equation:

6x(x+3)-9x(x+3)=0

We multiply parentheses

6x^2-9x^2+18x-27x=0

We add all the numbers together, and all the variables

-3x^2-9x=0

a = -3; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-3)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-3}=\frac{0}{-6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-3}=\frac{18}{-6}
=-3
$