3n^2+15n-150=0

Solution for 3n^2+15n-150=0 equation:

Simplifying
3n2 + 15n + -150 = 0

Reorder the terms:
-150 + 15n + 3n2 = 0

Solving
-150 + 15n + 3n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-50 + 5n + n2) = 0

Factor a trinomial.
3((-10 + -1n)(5 + -1n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-10 + -1n)' equal to zero and attempt to solve:

Simplifying
-10 + -1n = 0

Solving
-10 + -1n = 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 + -1n = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1n = 0 + 10
-1n = 0 + 10

Combine like terms: 0 + 10 = 10
-1n = 10

Divide each side by '-1'.
n = -10

Simplifying
n = -10
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 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 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {-10, 5}