Y=(3x+6)(4x+16)

Solution for Y=(3x+6)(4x+16) equation:

=(3Y+6)(4Y+16)

We move all terms to the left:

-((3Y+6)(4Y+16))=0

We multiply parentheses ..

-((+12Y^2+48Y+24Y+96))=0


We calculate terms in parentheses: -((+12Y^2+48Y+24Y+96)), so:

(+12Y^2+48Y+24Y+96)

We get rid of parentheses

12Y^2+48Y+24Y+96

We add all the numbers together, and all the variables

12Y^2+72Y+96

Back to the equation:

-(12Y^2+72Y+96)


We get rid of parentheses

-12Y^2-72Y-96=0

a = -12; b = -72; c = -96;
Δ = b2-4ac
Δ = -722-4·(-12)·(-96)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-24}{2*-12}=\frac{48}{-24}
=-2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+24}{2*-12}=\frac{96}{-24}
=-4
$