Y=(x-6)(x+2)

Solution for Y=(x-6)(x+2) equation:

=(Y-6)(Y+2)

We move all terms to the left:

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

We multiply parentheses ..

-((+Y^2+2Y-6Y-12))=0


We calculate terms in parentheses: -((+Y^2+2Y-6Y-12)), so:

(+Y^2+2Y-6Y-12)

We get rid of parentheses

Y^2+2Y-6Y-12

We add all the numbers together, and all the variables

Y^2-4Y-12

Back to the equation:

-(Y^2-4Y-12)


We get rid of parentheses

-Y^2+4Y+12=0

We add all the numbers together, and all the variables

-1Y^2+4Y+12=0

a = -1; b = 4; c = +12;
Δ = b2-4ac
Δ = 42-4·(-1)·12
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8}{2*-1}=\frac{-12}{-2}
=+6
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*-1}=\frac{4}{-2}
=-2
$