(n-15)(n+6)=n-15

Solution for (n-15)(n+6)=n-15 equation:

Simplifying
(n + -15)(n + 6) = n + -15

Reorder the terms:
(-15 + n)(n + 6) = n + -15

Reorder the terms:
(-15 + n)(6 + n) = n + -15

Multiply (-15 + n) * (6 + n)
(-15(6 + n) + n(6 + n)) = n + -15
((6 * -15 + n * -15) + n(6 + n)) = n + -15
((-90 + -15n) + n(6 + n)) = n + -15
(-90 + -15n + (6 * n + n * n)) = n + -15
(-90 + -15n + (6n + n2)) = n + -15

Combine like terms: -15n + 6n = -9n
(-90 + -9n + n2) = n + -15

Reorder the terms:
-90 + -9n + n2 = -15 + n

Solving
-90 + -9n + n2 = -15 + n

Solving for variable 'n'.

Reorder the terms:
-90 + 15 + -9n + -1n + n2 = -15 + n + 15 + -1n

Combine like terms: -90 + 15 = -75
-75 + -9n + -1n + n2 = -15 + n + 15 + -1n

Combine like terms: -9n + -1n = -10n
-75 + -10n + n2 = -15 + n + 15 + -1n

Reorder the terms:
-75 + -10n + n2 = -15 + 15 + n + -1n

Combine like terms: -15 + 15 = 0
-75 + -10n + n2 = 0 + n + -1n
-75 + -10n + n2 = n + -1n

Combine like terms: n + -1n = 0
-75 + -10n + n2 = 0

Factor a trinomial.
(-5 + -1n)(15 + -1n) = 0

Subproblem 1
Set the factor '(-5 + -1n)' equal to zero and attempt to solve:

Simplifying
-5 + -1n = 0

Solving
-5 + -1n = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1n = 0 + 5
-1n = 0 + 5

Combine like terms: 0 + 5 = 5
-1n = 5

Divide each side by '-1'.
n = -5

Simplifying
n = -5
Subproblem 2
Set the factor '(15 + -1n)' equal to zero and attempt to solve:

Simplifying
15 + -1n = 0

Solving
15 + -1n = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1n = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1n = 0 + -15
-1n = 0 + -15

Combine like terms: 0 + -15 = -15
-1n = -15

Divide each side by '-1'.
n = 15

Simplifying
n = 15
Solution
n = {-5, 15}