n^2-18n-22=-3

Solution for n^2-18n-22=-3 equation:

Simplifying
n2 + -18n + -22 = -3

Reorder the terms:
-22 + -18n + n2 = -3

Solving
-22 + -18n + n2 = -3

Solving for variable 'n'.

Reorder the terms:
-22 + 3 + -18n + n2 = -3 + 3

Combine like terms: -22 + 3 = -19
-19 + -18n + n2 = -3 + 3

Combine like terms: -3 + 3 = 0
-19 + -18n + n2 = 0

Factor a trinomial.
(-1 + -1n)(19 + -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 '(19 + -1n)' equal to zero and attempt to solve:

Simplifying
19 + -1n = 0

Solving
19 + -1n = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1n = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1n = 0 + -19
-1n = 0 + -19

Combine like terms: 0 + -19 = -19
-1n = -19

Divide each side by '-1'.
n = 19

Simplifying
n = 19
Solution
n = {-1, 19}