2n^2=20n-48

Solution for 2n^2=20n-48 equation:

Simplifying
2n2 = 20n + -48

Reorder the terms:
2n2 = -48 + 20n

Solving
2n2 = -48 + 20n

Solving for variable 'n'.

Reorder the terms:
48 + -20n + 2n2 = -48 + 20n + 48 + -20n

Reorder the terms:
48 + -20n + 2n2 = -48 + 48 + 20n + -20n

Combine like terms: -48 + 48 = 0
48 + -20n + 2n2 = 0 + 20n + -20n
48 + -20n + 2n2 = 20n + -20n

Combine like terms: 20n + -20n = 0
48 + -20n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + -10n + n2) = 0

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
n = {4, 6}