2n^2=48-4n

Solution for 2n^2=48-4n equation:

Simplifying
2n2 = 48 + -4n

Solving
2n2 = 48 + -4n

Solving for variable 'n'.

Reorder the terms:
-48 + 4n + 2n2 = 48 + -4n + -48 + 4n

Reorder the terms:
-48 + 4n + 2n2 = 48 + -48 + -4n + 4n

Combine like terms: 48 + -48 = 0
-48 + 4n + 2n2 = 0 + -4n + 4n
-48 + 4n + 2n2 = -4n + 4n

Combine like terms: -4n + 4n = 0
-48 + 4n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + 2n + n2) = 0

Factor a trinomial.
2((-6 + -1n)(4 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve:

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '6' to each side of the equation.
-6 + 6 + -1n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1n = 0 + 6
-1n = 0 + 6

Combine like terms: 0 + 6 = 6
-1n = 6

Divide each side by '-1'.
n = -6

Simplifying
n = -6
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-6, 4}