30=(15*n*(1+n))

Solution for 30=(15*n*(1+n)) equation:

Simplifying
30 = (15n(1 + n))
30 = ((1 * 15n + n * 15n))
30 = ((15n + 15n2))
30 = (15n + 15n2)

Remove parenthesis around (15n + 15n2)
30 = 15n + 15n2

Solving
30 = 15n + 15n2

Solving for variable 'n'.

Reorder the terms:
30 + -15n + -15n2 = 15n + -15n + 15n2 + -15n2

Combine like terms: 15n + -15n = 0
30 + -15n + -15n2 = 0 + 15n2 + -15n2
30 + -15n + -15n2 = 15n2 + -15n2

Combine like terms: 15n2 + -15n2 = 0
30 + -15n + -15n2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(2 + -1n + -1n2) = 0

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

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

Simplifying
2 + n = 0

Solving
2 + n = 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 + n = 0 + -2

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

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

Simplifying
n = -2
Solution
n = {1, -2}