A=(2x+1)(x+1)

Solution for A=(2x+1)(x+1) equation:

=(2A+1)(A+1)

We move all terms to the left:

-((2A+1)(A+1))=0

We multiply parentheses ..

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


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

(+2A^2+2A+A+1)

We get rid of parentheses

2A^2+2A+A+1

We add all the numbers together, and all the variables

2A^2+3A+1

Back to the equation:

-(2A^2+3A+1)


We get rid of parentheses

-2A^2-3A-1=0

a = -2; b = -3; c = -1;
Δ = b2-4ac
Δ = -32-4·(-2)·(-1)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-1}{2*-2}=\frac{2}{-4}
=-1/2
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+1}{2*-2}=\frac{4}{-4}
=-1
$