90=N(N+1)

Solution for 90=N(N+1) equation:

Simplifying
90 = N(N + 1)

Reorder the terms:
90 = N(1 + N)
90 = (1 * N + N * N)
90 = (1N + N2)

Solving
90 = 1N + N2

Solving for variable 'N'.

Reorder the terms:
90 + -1N + -1N2 = 1N + -1N + N2 + -1N2

Combine like terms: 1N + -1N = 0
90 + -1N + -1N2 = 0 + N2 + -1N2
90 + -1N + -1N2 = N2 + -1N2

Combine like terms: N2 + -1N2 = 0
90 + -1N + -1N2 = 0

Factor a trinomial.
(9 + -1N)(10 + N) = 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 + N)' equal to zero and attempt to solve:

Simplifying
10 + N = 0

Solving
10 + N = 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 + N = 0 + -10

Combine like terms: 10 + -10 = 0
0 + N = 0 + -10
N = 0 + -10

Combine like terms: 0 + -10 = -10
N = -10

Simplifying
N = -10
Solution
N = {9, -10}