(n-1)(n+9)=-21

Solution for (n-1)(n+9)=-21 equation:

Simplifying
(n + -1)(n + 9) = -21

Reorder the terms:
(-1 + n)(n + 9) = -21

Reorder the terms:
(-1 + n)(9 + n) = -21

Multiply (-1 + n) * (9 + n)
(-1(9 + n) + n(9 + n)) = -21
((9 * -1 + n * -1) + n(9 + n)) = -21
((-9 + -1n) + n(9 + n)) = -21
(-9 + -1n + (9 * n + n * n)) = -21
(-9 + -1n + (9n + n2)) = -21

Combine like terms: -1n + 9n = 8n
(-9 + 8n + n2) = -21

Solving
-9 + 8n + n2 = -21

Solving for variable 'n'.

Reorder the terms:
-9 + 21 + 8n + n2 = -21 + 21

Combine like terms: -9 + 21 = 12
12 + 8n + n2 = -21 + 21

Combine like terms: -21 + 21 = 0
12 + 8n + n2 = 0

Factor a trinomial.
(6 + n)(2 + n) = 0

Subproblem 1
Set the factor '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 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 + n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + n = 0 + -6
n = 0 + -6

Combine like terms: 0 + -6 = -6
n = -6

Simplifying
n = -6
Subproblem 2
Set the factor '(2 + n)' equal to zero and attempt to solve:

Simplifying
2 + n = 0

Solving
2 + n = 0

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

Add '-2' to each side of the equation.
2 + -2 + n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + n = 0 + -2
n = 0 + -2

Combine like terms: 0 + -2 = -2
n = -2

Simplifying
n = -2
Solution
n = {-6, -2}