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.
(-10 + -1n)(5 + -1n) = 0

Subproblem 1
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
Subproblem 2
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
Solution
n = {-10, 5}