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.
(-6 + -1n)(1 + -1n) = 0

Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve:

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1n = 0 + 6

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

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

Divide each side by '-1'.
n = -6

Simplifying
n = -6
Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

Solving
1 + -1n = 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 + -1n = 0 + -1

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

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

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

Simplifying
n = 1
Solution
n = {-6, 1}