3x(x-2)+3x(2x+1)=0

Solution for 3x(x-2)+3x(2x+1)=0 equation:

3x(x-2)+3x(2x+1)=0

We multiply parentheses

3x^2+6x^2-6x+3x=0

We add all the numbers together, and all the variables

9x^2-3x=0

a = 9; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·9·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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