(x-1)(2x+6)-(x-1)(3-x)=0

Solution for (x-1)(2x+6)-(x-1)(3-x)=0 equation:

(x-1)(2x+6)-(x-1)(3-x)=0

We add all the numbers together, and all the variables

(x-1)(2x+6)-(x-1)(-1x+3)=0

We multiply parentheses ..

(+2x^2+6x-2x-6)-(x-1)(-1x+3)=0

We get rid of parentheses

2x^2+6x-2x-(x-1)(-1x+3)-6=0

We multiply parentheses ..

2x^2-(-1x^2+3x+x-3)+6x-2x-6=0

We add all the numbers together, and all the variables

2x^2-(-1x^2+3x+x-3)+4x-6=0

We get rid of parentheses

2x^2+1x^2-3x-x+4x+3-6=0

We add all the numbers together, and all the variables

3x^2-3=0

a = 3; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·3·(-3)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*3}=\frac{-6}{6}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*3}=\frac{6}{6}
=1
$