-6(y+1)=(-2y)(-8)(-4y)

Solution for -6(y+1)=(-2y)(-8)(-4y) equation:

-6(y+1)=(-2y)(-8)(-4y)

We move all terms to the left:

-6(y+1)-((-2y)(-8)(-4y))=0

We multiply parentheses

-6y-((-2y)(-8)(-4y))-6=0

We multiply parentheses ..

-6y-((+16y)(-4y))-6=0


We calculate terms in parentheses: -((+16y)(-4y)), so:

(+16y)(-4y)

We multiply parentheses ..

(-64y^2)

We get rid of parentheses

-64y^2

Back to the equation:

-(-64y^2)


We get rid of parentheses

64y^2-6y-6=0

a = 64; b = -6; c = -6;
Δ = b2-4ac
Δ = -62-4·64·(-6)
Δ = 1572
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1572}=\sqrt{4*393}=\sqrt{4}*\sqrt{393}=2\sqrt{393}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{393}}{2*64}=\frac{6-2\sqrt{393}}{128}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{393}}{2*64}=\frac{6+2\sqrt{393}}{128}
$