-5=n(n-6)

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

Simplifying
-5 = n(n + -6)

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

Solving
-5 = -6n + n2

Solving for variable 'n'.

Reorder the terms:
-5 + 6n + -1n2 = -6n + 6n + n2 + -1n2

Combine like terms: -6n + 6n = 0
-5 + 6n + -1n2 = 0 + n2 + -1n2
-5 + 6n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-5 + 6n + -1n2 = 0

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

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

Simplifying
-5 + n = 0

Solving
-5 + n = 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 + n = 0 + 5

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

Combine like terms: 0 + 5 = 5
n = 5

Simplifying
n = 5
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 = {5, 1}