n(n-5)=50

Solution for n(n-5)=50 equation:

Simplifying
n(n + -5) = 50

Reorder the terms:
n(-5 + n) = 50
(-5 * n + n * n) = 50
(-5n + n2) = 50

Solving
-5n + n2 = 50

Solving for variable 'n'.

Reorder the terms:
-50 + -5n + n2 = 50 + -50

Combine like terms: 50 + -50 = 0
-50 + -5n + 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}