n^2=5n-6

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

Simplifying
n2 = 5n + -6

Reorder the terms:
n2 = -6 + 5n

Solving
n2 = -6 + 5n

Solving for variable 'n'.

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

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

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