-10n+5n(n+6)=

Solution for -10n+5n(n+6)= equation:

Simplifying
-10n + 5n(n + 6) = 0

Reorder the terms:
-10n + 5n(6 + n) = 0
-10n + (6 * 5n + n * 5n) = 0
-10n + (30n + 5n2) = 0

Combine like terms: -10n + 30n = 20n
20n + 5n2 = 0

Solving
20n + 5n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '5n'.
5n(4 + n) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 0

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

Add '-4' to each side of the equation.
4 + -4 + n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + n = 0 + -4
n = 0 + -4

Combine like terms: 0 + -4 = -4
n = -4

Simplifying
n = -4
Solution
n = {0, -4}