n^2-4n+13=10

Solution for n^2-4n+13=10 equation:

Simplifying
n2 + -4n + 13 = 10

Reorder the terms:
13 + -4n + n2 = 10

Solving
13 + -4n + n2 = 10

Solving for variable 'n'.

Reorder the terms:
13 + -10 + -4n + n2 = 10 + -10

Combine like terms: 13 + -10 = 3
3 + -4n + n2 = 10 + -10

Combine like terms: 10 + -10 = 0
3 + -4n + n2 = 0

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

Subproblem 1
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
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 = {1, 3}