n^2-14n+45=5

Solution for n^2-14n+45=5 equation:

Simplifying
n2 + -14n + 45 = 5

Reorder the terms:
45 + -14n + n2 = 5

Solving
45 + -14n + n2 = 5

Solving for variable 'n'.

Reorder the terms:
45 + -5 + -14n + n2 = 5 + -5

Combine like terms: 45 + -5 = 40
40 + -14n + n2 = 5 + -5

Combine like terms: 5 + -5 = 0
40 + -14n + n2 = 0

Factor a trinomial.
(4 + -1n)(10 + -1n) = 0

Subproblem 1
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Subproblem 2
Set the factor '(10 + -1n)' equal to zero and attempt to solve:

Simplifying
10 + -1n = 0

Solving
10 + -1n = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1n = 0 + -10
-1n = 0 + -10

Combine like terms: 0 + -10 = -10
-1n = -10

Divide each side by '-1'.
n = 10

Simplifying
n = 10
Solution
n = {4, 10}