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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((2x-1)(2x+3)), so:

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

We multiply parentheses ..

(+4x^2+6x-2x-3)

We get rid of parentheses

4x^2+6x-2x-3

We add all the numbers together, and all the variables

4x^2+4x-3

Back to the equation:

-(4x^2+4x-3)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2-11x+6=0

a = -2; b = -11; c = +6;
Δ = b2-4ac
Δ = -112-4·(-2)·6
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-13}{2*-2}=\frac{-2}{-4}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+13}{2*-2}=\frac{24}{-4}
=-6
$