(3x-2)(6-3x)=0

Solution for (3x-2)(6-3x)=0 equation:

(3x-2)(6-3x)=0

We add all the numbers together, and all the variables

(3x-2)(-3x+6)=0

We multiply parentheses ..

(-9x^2+18x+6x-12)=0

We get rid of parentheses

-9x^2+18x+6x-12=0

We add all the numbers together, and all the variables

-9x^2+24x-12=0

a = -9; b = 24; c = -12;
Δ = b2-4ac
Δ = 242-4·(-9)·(-12)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12}{2*-9}=\frac{-36}{-18}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12}{2*-9}=\frac{-12}{-18}
=2/3
$