90=(15*n*(1+n))

Solution for 90=(15*n*(1+n)) equation:

Simplifying
90 = (15n(1 + n))
90 = ((1 * 15n + n * 15n))
90 = ((15n + 15n2))
90 = (15n + 15n2)

Remove parenthesis around (15n + 15n2)
90 = 15n + 15n2

Solving
90 = 15n + 15n2

Solving for variable 'n'.

Reorder the terms:
90 + -15n + -15n2 = 15n + -15n + 15n2 + -15n2

Combine like terms: 15n + -15n = 0
90 + -15n + -15n2 = 0 + 15n2 + -15n2
90 + -15n + -15n2 = 15n2 + -15n2

Combine like terms: 15n2 + -15n2 = 0
90 + -15n + -15n2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(6 + -1n + -1n2) = 0

Factor a trinomial.
15((2 + -1n)(3 + n)) = 0

Ignore the factor 15.
Subproblem 1
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Subproblem 2
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 0

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

Add '-3' to each side of the equation.
3 + -3 + n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + n = 0 + -3
n = 0 + -3

Combine like terms: 0 + -3 = -3
n = -3

Simplifying
n = -3
Solution
n = {2, -3}