3n^2=-9n

Solution for 3n^2=-9n equation:

Simplifying
3n2 = -9n

Solving
3n2 = -9n

Solving for variable 'n'.

Reorder the terms:
9n + 3n2 = -9n + 9n

Combine like terms: -9n + 9n = 0
9n + 3n2 = 0

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

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

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 0

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

Add '-3' to each side of the equation.
3 + -3 + n = 0 + -3

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

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

Simplifying
n = -3
Solution
n = {0, -3}