(n-1)(n+8)=0

Solution for (n-1)(n+8)=0 equation:

Simplifying
(n + -1)(n + 8) = 0

Reorder the terms:
(-1 + n)(n + 8) = 0

Reorder the terms:
(-1 + n)(8 + n) = 0

Multiply (-1 + n) * (8 + n)
(-1(8 + n) + n(8 + n)) = 0
((8 * -1 + n * -1) + n(8 + n)) = 0
((-8 + -1n) + n(8 + n)) = 0
(-8 + -1n + (8 * n + n * n)) = 0
(-8 + -1n + (8n + n2)) = 0

Combine like terms: -1n + 8n = 7n
(-8 + 7n + n2) = 0

Solving
-8 + 7n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-8 + -1n)(1 + -1n) = 0

Subproblem 1
Set the factor '(-8 + -1n)' equal to zero and attempt to solve:

Simplifying
-8 + -1n = 0

Solving
-8 + -1n = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1n = 0 + 8
-1n = 0 + 8

Combine like terms: 0 + 8 = 8
-1n = 8

Divide each side by '-1'.
n = -8

Simplifying
n = -8
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 = {-8, 1}