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

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

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

We move all terms to the left:

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

We use the square of the difference formula

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

We multiply parentheses ..

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


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

(2x+1)(2x+1)

We multiply parentheses ..

(+4x^2+2x+2x+1)

We get rid of parentheses

4x^2+2x+2x+1

We add all the numbers together, and all the variables

4x^2+4x+1

Back to the equation:

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


We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2+2=0

a = -2; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-2)·2
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4}{2*-2}=\frac{-4}{-4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4}{2*-2}=\frac{4}{-4}
=-1
$