(n+10)(n-9)=0

Solution for (n+10)(n-9)=0 equation:

Simplifying
(n + 10)(n + -9) = 0

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

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

Multiply (10 + n) * (-9 + n)
(10(-9 + n) + n(-9 + n)) = 0
((-9 * 10 + n * 10) + n(-9 + n)) = 0
((-90 + 10n) + n(-9 + n)) = 0
(-90 + 10n + (-9 * n + n * n)) = 0
(-90 + 10n + (-9n + n2)) = 0

Combine like terms: 10n + -9n = 1n
(-90 + 1n + n2) = 0

Solving
-90 + 1n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-10 + -1n)(9 + -1n) = 0

Subproblem 1
Set the factor '(-10 + -1n)' equal to zero and attempt to solve:

Simplifying
-10 + -1n = 0

Solving
-10 + -1n = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1n = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1n = 0 + 10
-1n = 0 + 10

Combine like terms: 0 + 10 = 10
-1n = 10

Divide each side by '-1'.
n = -10

Simplifying
n = -10
Subproblem 2
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
Solution
n = {-10, 9}