5n^2-2n=16

Solution for 5n^2-2n=16 equation:

Simplifying
5n2 + -2n = 16

Reorder the terms:
-2n + 5n2 = 16

Solving
-2n + 5n2 = 16

Solving for variable 'n'.

Reorder the terms:
-16 + -2n + 5n2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + -2n + 5n2 = 0

Factor a trinomial.
(-8 + -5n)(2 + -1n) = 0

Subproblem 1
Set the factor '(-8 + -5n)' equal to zero and attempt to solve:

Simplifying
-8 + -5n = 0

Solving
-8 + -5n = 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 + -5n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -5n = 0 + 8
-5n = 0 + 8

Combine like terms: 0 + 8 = 8
-5n = 8

Divide each side by '-5'.
n = -1.6

Simplifying
n = -1.6
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {-1.6, 2}