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

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

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

We multiply parentheses

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2+x-12=0

a = 1; b = 1; c = -12;
Δ = b2-4ac
Δ = 12-4·1·(-12)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7}{2*1}=\frac{-8}{2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*1}=\frac{6}{2}
=3
$