90=n(2n+3)

Solution for 90=n(2n+3) equation:

Simplifying
90 = n(2n + 3)

Reorder the terms:
90 = n(3 + 2n)
90 = (3 * n + 2n * n)
90 = (3n + 2n2)

Solving
90 = 3n + 2n2

Solving for variable 'n'.

Reorder the terms:
90 + -3n + -2n2 = 3n + -3n + 2n2 + -2n2

Combine like terms: 3n + -3n = 0
90 + -3n + -2n2 = 0 + 2n2 + -2n2
90 + -3n + -2n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
90 + -3n + -2n2 = 0

Factor a trinomial.
(6 + -1n)(15 + 2n) = 0

Subproblem 1
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

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

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

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Subproblem 2
Set the factor '(15 + 2n)' equal to zero and attempt to solve:

Simplifying
15 + 2n = 0

Solving
15 + 2n = 0

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

Add '-15' to each side of the equation.
15 + -15 + 2n = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 2n = 0 + -15
2n = 0 + -15

Combine like terms: 0 + -15 = -15
2n = -15

Divide each side by '2'.
n = -7.5

Simplifying
n = -7.5
Solution
n = {6, -7.5}