A=(x+5)(3x+6)

Solution for A=(x+5)(3x+6) equation:

=(A+5)(3A+6)

We move all terms to the left:

-((A+5)(3A+6))=0

We multiply parentheses ..

-((+3A^2+6A+15A+30))=0


We calculate terms in parentheses: -((+3A^2+6A+15A+30)), so:

(+3A^2+6A+15A+30)

We get rid of parentheses

3A^2+6A+15A+30

We add all the numbers together, and all the variables

3A^2+21A+30

Back to the equation:

-(3A^2+21A+30)


We get rid of parentheses

-3A^2-21A-30=0

a = -3; b = -21; c = -30;
Δ = b2-4ac
Δ = -212-4·(-3)·(-30)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-9}{2*-3}=\frac{12}{-6}
=-2
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+9}{2*-3}=\frac{30}{-6}
=-5
$