-5n(n-1)=5-5n

Solution for -5n(n-1)=5-5n equation:

Simplifying
-5n(n + -1) = 5 + -5n

Reorder the terms:
-5n(-1 + n) = 5 + -5n
(-1 * -5n + n * -5n) = 5 + -5n
(5n + -5n2) = 5 + -5n

Solving
5n + -5n2 = 5 + -5n

Solving for variable 'n'.

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

Combine like terms: 5n + 5n = 10n
-5 + 10n + -5n2 = 5 + -5n + -5 + 5n

Reorder the terms:
-5 + 10n + -5n2 = 5 + -5 + -5n + 5n

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

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

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + 2n + -1n2) = 0

Factor a trinomial.
5((-1 + n)(1 + -1n)) = 0

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

Simplifying
-1 + n = 0

Solving
-1 + n = 0

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

Add '1' to each side of the equation.
-1 + 1 + n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + n = 0 + 1
n = 0 + 1

Combine like terms: 0 + 1 = 1
n = 1

Simplifying
n = 1
Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1n = 0 + -1
-1n = 0 + -1

Combine like terms: 0 + -1 = -1
-1n = -1

Divide each side by '-1'.
n = 1

Simplifying
n = 1
Solution
n = {1, 1}