-3(4n+2)=-4n+-2n(4n-6)

Solution for -3(4n+2)=-4n+-2n(4n-6) equation:

-3(4n+2)=-4n+-2n(4n-6)

We move all terms to the left:

-3(4n+2)-(-4n+-2n(4n-6))=0

We use the square of the difference formula

-3(4n+2)-(-4n-2n(4n-6))=0

We multiply parentheses

-12n-(-4n-2n(4n-6))-6=0


We calculate terms in parentheses: -(-4n-2n(4n-6)), so:

-4n-2n(4n-6)

We multiply parentheses

-8n^2-4n+12n

We add all the numbers together, and all the variables

-8n^2+8n

Back to the equation:

-(-8n^2+8n)


We get rid of parentheses

8n^2-8n-12n-6=0

We add all the numbers together, and all the variables

8n^2-20n-6=0

a = 8; b = -20; c = -6;
Δ = b2-4ac
Δ = -202-4·8·(-6)
Δ = 592
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{37}}{2*8}=\frac{20-4\sqrt{37}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{37}}{2*8}=\frac{20+4\sqrt{37}}{16}
$