(2x+1)(x-1)=(4x-1)(x+3)

Solution for (2x+1)(x-1)=(4x-1)(x+3) equation:

(2x+1)(x-1)=(4x-1)(x+3)

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((4x-1)(x+3)), so:

(4x-1)(x+3)

We multiply parentheses ..

(+4x^2+12x-1x-3)

We get rid of parentheses

4x^2+12x-1x-3

We add all the numbers together, and all the variables

4x^2+11x-3

Back to the equation:

-(4x^2+11x-3)


We get rid of parentheses

2x^2-4x^2-2x+x-11x-1+3=0

We add all the numbers together, and all the variables

-2x^2-12x+2=0

a = -2; b = -12; c = +2;
Δ = b2-4ac
Δ = -122-4·(-2)·2
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{10}}{2*-2}=\frac{12-4\sqrt{10}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{10}}{2*-2}=\frac{12+4\sqrt{10}}{-4}
$