4n(12n-6)=6(-4+5n)+18n

Solution for 4n(12n-6)=6(-4+5n)+18n equation:

4n(12n-6)=6(-4+5n)+18n

We move all terms to the left:

4n(12n-6)-(6(-4+5n)+18n)=0

We add all the numbers together, and all the variables

4n(12n-6)-(6(5n-4)+18n)=0

We multiply parentheses

48n^2-24n-(6(5n-4)+18n)=0


We calculate terms in parentheses: -(6(5n-4)+18n), so:

6(5n-4)+18n

We add all the numbers together, and all the variables

18n+6(5n-4)

We multiply parentheses

18n+30n-24

We add all the numbers together, and all the variables

48n-24

Back to the equation:

-(48n-24)


We get rid of parentheses

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

We add all the numbers together, and all the variables

48n^2-72n+24=0

a = 48; b = -72; c = +24;
Δ = b2-4ac
Δ = -722-4·48·24
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-24}{2*48}=\frac{48}{96}
=1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+24}{2*48}=\frac{96}{96}
=1
$