Y=4(x+2)(x-1)

Solution for Y=4(x+2)(x-1) equation:

=4(Y+2)(Y-1)

We move all terms to the left:

-(4(Y+2)(Y-1))=0

We multiply parentheses ..

-(4(+Y^2-1Y+2Y-2))=0


We calculate terms in parentheses: -(4(+Y^2-1Y+2Y-2)), so:

4(+Y^2-1Y+2Y-2)

We multiply parentheses

4Y^2-4Y+8Y-8

We add all the numbers together, and all the variables

4Y^2+4Y-8

Back to the equation:

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


We get rid of parentheses

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

a = -4; b = -4; c = +8;
Δ = b2-4ac
Δ = -42-4·(-4)·8
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-12}{2*-4}=\frac{-8}{-8}
=1
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+12}{2*-4}=\frac{16}{-8}
=-2
$