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

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

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

We add all the numbers together, and all the variables

(3x-6)(-1x+3)=0

We multiply parentheses ..

(-3x^2+9x+6x-18)=0

We get rid of parentheses

-3x^2+9x+6x-18=0

We add all the numbers together, and all the variables

-3x^2+15x-18=0

a = -3; b = 15; c = -18;
Δ = b2-4ac
Δ = 152-4·(-3)·(-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{-(15)-3}{2*-3}=\frac{-18}{-6}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3}{2*-3}=\frac{-12}{-6}
=+2
$