A=(3x+7)(2x+3)

Solution for A=(3x+7)(2x+3) equation:

=(3A+7)(2A+3)

We move all terms to the left:

-((3A+7)(2A+3))=0

We multiply parentheses ..

-((+6A^2+9A+14A+21))=0


We calculate terms in parentheses: -((+6A^2+9A+14A+21)), so:

(+6A^2+9A+14A+21)

We get rid of parentheses

6A^2+9A+14A+21

We add all the numbers together, and all the variables

6A^2+23A+21

Back to the equation:

-(6A^2+23A+21)


We get rid of parentheses

-6A^2-23A-21=0

a = -6; b = -23; c = -21;
Δ = b2-4ac
Δ = -232-4·(-6)·(-21)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-5}{2*-6}=\frac{18}{-12}
=-1+1/2
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+5}{2*-6}=\frac{28}{-12}
=-2+1/3
$