n(n-15)=-50

Solution for n(n-15)=-50 equation:

Simplifying
n(n + -15) = -50

Reorder the terms:
n(-15 + n) = -50
(-15 * n + n * n) = -50
(-15n + n2) = -50

Solving
-15n + n2 = -50

Solving for variable 'n'.

Reorder the terms:
50 + -15n + n2 = -50 + 50

Combine like terms: -50 + 50 = 0
50 + -15n + n2 = 0

Factor a trinomial.
(5 + -1n)(10 + -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 '(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
Solution
n = {5, 10}