n^2-8n+33=3+3n

Solution for n^2-8n+33=3+3n equation:

Simplifying
n2 + -8n + 33 = 3 + 3n

Reorder the terms:
33 + -8n + n2 = 3 + 3n

Solving
33 + -8n + n2 = 3 + 3n

Solving for variable 'n'.

Reorder the terms:
33 + -3 + -8n + -3n + n2 = 3 + 3n + -3 + -3n

Combine like terms: 33 + -3 = 30
30 + -8n + -3n + n2 = 3 + 3n + -3 + -3n

Combine like terms: -8n + -3n = -11n
30 + -11n + n2 = 3 + 3n + -3 + -3n

Reorder the terms:
30 + -11n + n2 = 3 + -3 + 3n + -3n

Combine like terms: 3 + -3 = 0
30 + -11n + n2 = 0 + 3n + -3n
30 + -11n + n2 = 3n + -3n

Combine like terms: 3n + -3n = 0
30 + -11n + n2 = 0

Factor a trinomial.
(5 + -1n)(6 + -1n) = 0

Subproblem 1
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
Subproblem 2
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
Solution
n = {5, 6}