0=n^2-5n+6

Solution for 0=n^2-5n+6 equation:

Simplifying
0 = n2 + -5n + 6

Reorder the terms:
0 = 6 + -5n + n2

Solving
0 = 6 + -5n + n2

Solving for variable 'n'.

Combine like terms: 0 + -6 = -6
-6 + 5n + -1n2 = 6 + -5n + n2 + -6 + 5n + -1n2

Reorder the terms:
-6 + 5n + -1n2 = 6 + -6 + -5n + 5n + n2 + -1n2

Combine like terms: 6 + -6 = 0
-6 + 5n + -1n2 = 0 + -5n + 5n + n2 + -1n2
-6 + 5n + -1n2 = -5n + 5n + n2 + -1n2

Combine like terms: -5n + 5n = 0
-6 + 5n + -1n2 = 0 + n2 + -1n2
-6 + 5n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-6 + 5n + -1n2 = 0

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

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

Simplifying
-3 + n = 0

Solving
-3 + n = 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 + n = 0 + 3

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

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

Simplifying
n = 3
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 = {3, 2}