N^2+6=5N

Solution for N^2+6=5N equation:

Simplifying
N2 + 6 = 5N

Reorder the terms:
6 + N2 = 5N

Solving
6 + N2 = 5N

Solving for variable 'N'.

Reorder the terms:
6 + -5N + N2 = 5N + -5N

Combine like terms: 5N + -5N = 0
6 + -5N + N2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
N = {2, 3}