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

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

=(Y+3)(Y-6)

We move all terms to the left:

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

We multiply parentheses ..

-((+Y^2-6Y+3Y-18))=0


We calculate terms in parentheses: -((+Y^2-6Y+3Y-18)), so:

(+Y^2-6Y+3Y-18)

We get rid of parentheses

Y^2-6Y+3Y-18

We add all the numbers together, and all the variables

Y^2-3Y-18

Back to the equation:

-(Y^2-3Y-18)


We get rid of parentheses

-Y^2+3Y+18=0

We add all the numbers together, and all the variables

-1Y^2+3Y+18=0

a = -1; b = 3; c = +18;
Δ = b2-4ac
Δ = 32-4·(-1)·18
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*-1}=\frac{-12}{-2}
=+6
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+9}{2*-1}=\frac{6}{-2}
=-3
$