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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We multiply parentheses ..

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

We add all the numbers together, and all the variables

2x^2+(+2x^2-2x-1x+1)+5x-3=0

We get rid of parentheses

2x^2+2x^2-2x-1x+5x+1-3=0

We add all the numbers together, and all the variables

4x^2+2x-2=0

a = 4; b = 2; c = -2;
Δ = b2-4ac
Δ = 22-4·4·(-2)
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{-(2)-6}{2*4}=\frac{-8}{8}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6}{2*4}=\frac{4}{8}
=1/2
$