4(6-4n)=-6n+6(2n-7)n=3

Solution for 4(6-4n)=-6n+6(2n-7)n=3 equation:

4(6-4n)=-6n+6(2n-7)n=3

We move all terms to the left:

4(6-4n)-(-6n+6(2n-7)n)=0

We add all the numbers together, and all the variables

4(-4n+6)-(-6n+6(2n-7)n)=0

We multiply parentheses

-16n-(-6n+6(2n-7)n)+24=0


We calculate terms in parentheses: -(-6n+6(2n-7)n), so:

-6n+6(2n-7)n

We multiply parentheses

12n^2-6n-42n

We add all the numbers together, and all the variables

12n^2-48n

Back to the equation:

-(12n^2-48n)


We get rid of parentheses

-12n^2-16n+48n+24=0

We add all the numbers together, and all the variables

-12n^2+32n+24=0

a = -12; b = 32; c = +24;
Δ = b2-4ac
Δ = 322-4·(-12)·24
Δ = 2176
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:

$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-8\sqrt{34}}{2*-12}=\frac{-32-8\sqrt{34}}{-24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8\sqrt{34}}{2*-12}=\frac{-32+8\sqrt{34}}{-24}
$