9n^2+75n+150=0

Solution for 9n^2+75n+150=0 equation:

Simplifying
9n2 + 75n + 150 = 0

Reorder the terms:
150 + 75n + 9n2 = 0

Solving
150 + 75n + 9n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(50 + 25n + 3n2) = 0

Factor a trinomial.
3((5 + n)(10 + 3n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + n)' equal to zero and attempt to solve:

Simplifying
5 + n = 0

Solving
5 + n = 0

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

Add '-5' to each side of the equation.
5 + -5 + n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + n = 0 + -5
n = 0 + -5

Combine like terms: 0 + -5 = -5
n = -5

Simplifying
n = -5
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 = {-5, -3.333333333}