3n^2+37n+90=0

Solution for 3n^2+37n+90=0 equation:

Simplifying
3n2 + 37n + 90 = 0

Reorder the terms:
90 + 37n + 3n2 = 0

Solving
90 + 37n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(9 + n)(10 + 3n) = 0

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

Simplifying
9 + n = 0

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

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

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

Simplifying
n = -9
Subproblem 2
Set the factor '(10 + 3n)' equal to zero and attempt to solve:

Simplifying
10 + 3n = 0

Solving
10 + 3n = 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 + 3n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 3n = 0 + -10
3n = 0 + -10

Combine like terms: 0 + -10 = -10
3n = -10

Divide each side by '3'.
n = -3.333333333

Simplifying
n = -3.333333333
Solution
n = {-9, -3.333333333}