3n^2+5=16n

Solution for 3n^2+5=16n equation:

Simplifying
3n2 + 5 = 16n

Reorder the terms:
5 + 3n2 = 16n

Solving
5 + 3n2 = 16n

Solving for variable 'n'.

Reorder the terms:
5 + -16n + 3n2 = 16n + -16n

Combine like terms: 16n + -16n = 0
5 + -16n + 3n2 = 0

Factor a trinomial.
(1 + -3n)(5 + -1n) = 0

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

Simplifying
1 + -3n = 0

Solving
1 + -3n = 0

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

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

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

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

Divide each side by '-3'.
n = 0.3333333333

Simplifying
n = 0.3333333333
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {0.3333333333, 5}