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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-6x^2+21x-18=0

a = -6; b = 21; c = -18;
Δ = b2-4ac
Δ = 212-4·(-6)·(-18)
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{-(21)-3}{2*-6}=\frac{-24}{-12}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3}{2*-6}=\frac{-18}{-12}
=1+1/2
$