Y=3(x+5)(x-3)

Solution for Y=3(x+5)(x-3) equation:

=3(Y+5)(Y-3)

We move all terms to the left:

-(3(Y+5)(Y-3))=0

We multiply parentheses ..

-(3(+Y^2-3Y+5Y-15))=0


We calculate terms in parentheses: -(3(+Y^2-3Y+5Y-15)), so:

3(+Y^2-3Y+5Y-15)

We multiply parentheses

3Y^2-9Y+15Y-45

We add all the numbers together, and all the variables

3Y^2+6Y-45

Back to the equation:

-(3Y^2+6Y-45)


We get rid of parentheses

-3Y^2-6Y+45=0

a = -3; b = -6; c = +45;
Δ = b2-4ac
Δ = -62-4·(-3)·45
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-24}{2*-3}=\frac{-18}{-6}
=+3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+24}{2*-3}=\frac{30}{-6}
=-5
$