(n-15)*(15-n)=

Solution for (n-15)*(15-n)= equation:

Simplifying
(n + -15)(15 + -1n) = 0

Reorder the terms:
(-15 + n)(15 + -1n) = 0

Multiply (-15 + n) * (15 + -1n)
(-15(15 + -1n) + n(15 + -1n)) = 0
((15 * -15 + -1n * -15) + n(15 + -1n)) = 0
((-225 + 15n) + n(15 + -1n)) = 0
(-225 + 15n + (15 * n + -1n * n)) = 0
(-225 + 15n + (15n + -1n2)) = 0

Combine like terms: 15n + 15n = 30n
(-225 + 30n + -1n2) = 0

Solving
-225 + 30n + -1n2 = 0

Solving for variable 'n'.

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

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

Simplifying
-15 + n = 0

Solving
-15 + n = 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 + n = 0 + 15

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

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

Simplifying
n = 15
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 = {15, 15}