n^2-11n+32=4

Solution for n^2-11n+32=4 equation:

Simplifying
n2 + -11n + 32 = 4

Reorder the terms:
32 + -11n + n2 = 4

Solving
32 + -11n + n2 = 4

Solving for variable 'n'.

Reorder the terms:
32 + -4 + -11n + n2 = 4 + -4

Combine like terms: 32 + -4 = 28
28 + -11n + n2 = 4 + -4

Combine like terms: 4 + -4 = 0
28 + -11n + n2 = 0

Factor a trinomial.
(4 + -1n)(7 + -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 '(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 = {4, 7}