5n^2=-6n

Solution for 5n^2=-6n equation:

Simplifying
5n2 = -6n

Solving
5n2 = -6n

Solving for variable 'n'.

Reorder the terms:
6n + 5n2 = -6n + 6n

Combine like terms: -6n + 6n = 0
6n + 5n2 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(6 + 5n) = 0

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 '(6 + 5n)' equal to zero and attempt to solve:

Simplifying
6 + 5n = 0

Solving
6 + 5n = 0

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

Add '-6' to each side of the equation.
6 + -6 + 5n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5n = 0 + -6
5n = 0 + -6

Combine like terms: 0 + -6 = -6
5n = -6

Divide each side by '5'.
n = -1.2

Simplifying
n = -1.2
Solution
n = {0, -1.2}