Y=(3x+6)(6x-18)

Solution for Y=(3x+6)(6x-18) equation:

=(3Y+6)(6Y-18)

We move all terms to the left:

-((3Y+6)(6Y-18))=0

We multiply parentheses ..

-((+18Y^2-54Y+36Y-108))=0


We calculate terms in parentheses: -((+18Y^2-54Y+36Y-108)), so:

(+18Y^2-54Y+36Y-108)

We get rid of parentheses

18Y^2-54Y+36Y-108

We add all the numbers together, and all the variables

18Y^2-18Y-108

Back to the equation:

-(18Y^2-18Y-108)


We get rid of parentheses

-18Y^2+18Y+108=0

a = -18; b = 18; c = +108;
Δ = b2-4ac
Δ = 182-4·(-18)·108
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-90}{2*-18}=\frac{-108}{-36}
=+3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+90}{2*-18}=\frac{72}{-36}
=-2
$