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

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

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

We move all terms to the left:

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

We get rid of 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^2-3x=0

a = 1; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·1·0
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{-(-3)-3}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*1}=\frac{6}{2}
=3
$