n^2-10n-20=-9

Solution for n^2-10n-20=-9 equation:

Simplifying
n2 + -10n + -20 = -9

Reorder the terms:
-20 + -10n + n2 = -9

Solving
-20 + -10n + n2 = -9

Solving for variable 'n'.

Reorder the terms:
-20 + 9 + -10n + n2 = -9 + 9

Combine like terms: -20 + 9 = -11
-11 + -10n + n2 = -9 + 9

Combine like terms: -9 + 9 = 0
-11 + -10n + n2 = 0

Factor a trinomial.
(-1 + -1n)(11 + -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 '(11 + -1n)' equal to zero and attempt to solve:

Simplifying
11 + -1n = 0

Solving
11 + -1n = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1n = 0 + -11
-1n = 0 + -11

Combine like terms: 0 + -11 = -11
-1n = -11

Divide each side by '-1'.
n = 11

Simplifying
n = 11
Solution
n = {-1, 11}