n(n+1)=10n

Solution for n(n+1)=10n equation:

Simplifying
n(n + 1) = 10n

Reorder the terms:
n(1 + n) = 10n
(1 * n + n * n) = 10n
(1n + n2) = 10n

Solving
1n + n2 = 10n

Solving for variable 'n'.

Reorder the terms:
1n + -10n + n2 = 10n + -10n

Combine like terms: 1n + -10n = -9n
-9n + n2 = 10n + -10n

Combine like terms: 10n + -10n = 0
-9n + n2 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-9 + n) = 0

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 '(-9 + n)' equal to zero and attempt to solve:

Simplifying
-9 + n = 0

Solving
-9 + n = 0

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

Add '9' to each side of the equation.
-9 + 9 + n = 0 + 9

Combine like terms: -9 + 9 = 0
0 + n = 0 + 9
n = 0 + 9

Combine like terms: 0 + 9 = 9
n = 9

Simplifying
n = 9
Solution
n = {0, 9}