n(n-1)=90

Solution for n(n-1)=90 equation:

Simplifying
n(n + -1) = 90

Reorder the terms:
n(-1 + n) = 90
(-1 * n + n * n) = 90
(-1n + n2) = 90

Solving
-1n + n2 = 90

Solving for variable 'n'.

Reorder the terms:
-90 + -1n + n2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + -1n + n2 = 0

Factor a trinomial.
(-9 + -1n)(10 + -1n) = 0

Subproblem 1
Set the factor '(-9 + -1n)' equal to zero and attempt to solve:

Simplifying
-9 + -1n = 0

Solving
-9 + -1n = 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 + -1n = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1n = 0 + 9
-1n = 0 + 9

Combine like terms: 0 + 9 = 9
-1n = 9

Divide each side by '-1'.
n = -9

Simplifying
n = -9
Subproblem 2
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
Solution
n = {-9, 10}