Y=3(x+4)(x-6)

Solution for Y=3(x+4)(x-6) equation:

=3(Y+4)(Y-6)

We move all terms to the left:

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

We multiply parentheses ..

-(3(+Y^2-6Y+4Y-24))=0


We calculate terms in parentheses: -(3(+Y^2-6Y+4Y-24)), so:

3(+Y^2-6Y+4Y-24)

We multiply parentheses

3Y^2-18Y+12Y-72

We add all the numbers together, and all the variables

3Y^2-6Y-72

Back to the equation:

-(3Y^2-6Y-72)


We get rid of parentheses

-3Y^2+6Y+72=0

a = -3; b = 6; c = +72;
Δ = b2-4ac
Δ = 62-4·(-3)·72
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-30}{2*-3}=\frac{-36}{-6}
=+6
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+30}{2*-3}=\frac{24}{-6}
=-4
$