Y=4(x+8)(x-6)

Solution for Y=4(x+8)(x-6) equation:

=4(Y+8)(Y-6)

We move all terms to the left:

-(4(Y+8)(Y-6))=0

We multiply parentheses ..

-(4(+Y^2-6Y+8Y-48))=0


We calculate terms in parentheses: -(4(+Y^2-6Y+8Y-48)), so:

4(+Y^2-6Y+8Y-48)

We multiply parentheses

4Y^2-24Y+32Y-192

We add all the numbers together, and all the variables

4Y^2+8Y-192

Back to the equation:

-(4Y^2+8Y-192)


We get rid of parentheses

-4Y^2-8Y+192=0

a = -4; b = -8; c = +192;
Δ = b2-4ac
Δ = -82-4·(-4)·192
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-56}{2*-4}=\frac{-48}{-8}
=+6
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+56}{2*-4}=\frac{64}{-8}
=-8
$