3p(p-2)-2p(3p-2)=0

Solution for 3p(p-2)-2p(3p-2)=0 equation:

3p(p-2)-2p(3p-2)=0

We multiply parentheses

3p^2-6p^2-6p+4p=0

We add all the numbers together, and all the variables

-3p^2-2p=0

a = -3; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-3)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-3}=\frac{0}{-6}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-3}=\frac{4}{-6}
=-2/3
$