2n^2=10n+48

Solution for 2n^2=10n+48 equation:

Simplifying
2n2 = 10n + 48

Reorder the terms:
2n2 = 48 + 10n

Solving
2n2 = 48 + 10n

Solving for variable 'n'.

Reorder the terms:
-48 + -10n + 2n2 = 48 + 10n + -48 + -10n

Reorder the terms:
-48 + -10n + 2n2 = 48 + -48 + 10n + -10n

Combine like terms: 48 + -48 = 0
-48 + -10n + 2n2 = 0 + 10n + -10n
-48 + -10n + 2n2 = 10n + -10n

Combine like terms: 10n + -10n = 0
-48 + -10n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + -5n + n2) = 0

Factor a trinomial.
2((-3 + -1n)(8 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve:

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1n = 0 + 3
-1n = 0 + 3

Combine like terms: 0 + 3 = 3
-1n = 3

Divide each side by '-1'.
n = -3

Simplifying
n = -3
Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve:

Simplifying
8 + -1n = 0

Solving
8 + -1n = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1n = 0 + -8
-1n = 0 + -8

Combine like terms: 0 + -8 = -8
-1n = -8

Divide each side by '-1'.
n = 8

Simplifying
n = 8
Solution
n = {-3, 8}