n^2-13n+46=4

Solution for n^2-13n+46=4 equation:

Simplifying
n2 + -13n + 46 = 4

Reorder the terms:
46 + -13n + n2 = 4

Solving
46 + -13n + n2 = 4

Solving for variable 'n'.

Reorder the terms:
46 + -4 + -13n + n2 = 4 + -4

Combine like terms: 46 + -4 = 42
42 + -13n + n2 = 4 + -4

Combine like terms: 4 + -4 = 0
42 + -13n + n2 = 0

Factor a trinomial.
(6 + -1n)(7 + -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 '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {6, 7}