Y=(3x+6)(x-1)

Solution for Y=(3x+6)(x-1) equation:

=(3Y+6)(Y-1)

We move all terms to the left:

-((3Y+6)(Y-1))=0

We multiply parentheses ..

-((+3Y^2-3Y+6Y-6))=0


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

(+3Y^2-3Y+6Y-6)

We get rid of parentheses

3Y^2-3Y+6Y-6

We add all the numbers together, and all the variables

3Y^2+3Y-6

Back to the equation:

-(3Y^2+3Y-6)


We get rid of parentheses

-3Y^2-3Y+6=0

a = -3; b = -3; c = +6;
Δ = b2-4ac
Δ = -32-4·(-3)·6
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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