(n+9)(n-6)=-50

Solution for (n+9)(n-6)=-50 equation:

Simplifying
(n + 9)(n + -6) = -50

Reorder the terms:
(9 + n)(n + -6) = -50

Reorder the terms:
(9 + n)(-6 + n) = -50

Multiply (9 + n) * (-6 + n)
(9(-6 + n) + n(-6 + n)) = -50
((-6 * 9 + n * 9) + n(-6 + n)) = -50
((-54 + 9n) + n(-6 + n)) = -50
(-54 + 9n + (-6 * n + n * n)) = -50
(-54 + 9n + (-6n + n2)) = -50

Combine like terms: 9n + -6n = 3n
(-54 + 3n + n2) = -50

Solving
-54 + 3n + n2 = -50

Solving for variable 'n'.

Reorder the terms:
-54 + 50 + 3n + n2 = -50 + 50

Combine like terms: -54 + 50 = -4
-4 + 3n + n2 = -50 + 50

Combine like terms: -50 + 50 = 0
-4 + 3n + n2 = 0

Factor a trinomial.
(-4 + -1n)(1 + -1n) = 0

Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve:

Simplifying
-4 + -1n = 0

Solving
-4 + -1n = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1n = 0 + 4
-1n = 0 + 4

Combine like terms: 0 + 4 = 4
-1n = 4

Divide each side by '-1'.
n = -4

Simplifying
n = -4
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 = {-4, 1}