(n-1)(n+9)=0

Solution for (n-1)(n+9)=0 equation:

Simplifying
(n + -1)(n + 9) = 0

Reorder the terms:
(-1 + n)(n + 9) = 0

Reorder the terms:
(-1 + n)(9 + n) = 0

Multiply (-1 + n) * (9 + n)
(-1(9 + n) + n(9 + n)) = 0
((9 * -1 + n * -1) + n(9 + n)) = 0
((-9 + -1n) + n(9 + n)) = 0
(-9 + -1n + (9 * n + n * n)) = 0
(-9 + -1n + (9n + n2)) = 0

Combine like terms: -1n + 9n = 8n
(-9 + 8n + n2) = 0

Solving
-9 + 8n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-9 + -1n)(1 + -1n) = 0

Subproblem 1
Set the factor '(-9 + -1n)' equal to zero and attempt to solve:

Simplifying
-9 + -1n = 0

Solving
-9 + -1n = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1n = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1n = 0 + 9
-1n = 0 + 9

Combine like terms: 0 + 9 = 9
-1n = 9

Divide each side by '-1'.
n = -9

Simplifying
n = -9
Subproblem 2
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
Solution
n = {-9, 1}