Answer: n = 0
n = 3
n = - 5
Step-by-step explanation:
The given cubic equation is expressed as
n³ + 2n² - 15n = 0
Since n is common to each term, we would factorize n out. It becomes
n(n² + 2n - 15) = 0
n = 0 or
n² + 2n - 15 = 0
To further factorize the quadratic equation, we would would find two numbers such that their sum or difference is 2n and their product is - 15n². The two numbers are 5n and - 3n. Therefore,
n² + 5n - 3n - 15 = 0
n(n + 5) - 3(n + 5) = 0
(n - 3)(n + 5) = 0
n = 3 or n = - 5
