2n^2-38n+96=

Solution for 2n^2-38n+96= equation:

Simplifying
2n2 + -38n + 96 = 0

Reorder the terms:
96 + -38n + 2n2 = 0

Solving
96 + -38n + 2n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(48 + -19n + n2) = 0

Factor a trinomial.
2((3 + -1n)(16 + -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 '(16 + -1n)' equal to zero and attempt to solve:

Simplifying
16 + -1n = 0

Solving
16 + -1n = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1n = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1n = 0 + -16
-1n = 0 + -16

Combine like terms: 0 + -16 = -16
-1n = -16

Divide each side by '-1'.
n = 16

Simplifying
n = 16
Solution
n = {3, 16}