6n^2=-3n

Solution for 6n^2=-3n equation:

Simplifying
6n2 = -3n

Solving
6n2 = -3n

Solving for variable 'n'.

Reorder the terms:
3n + 6n2 = -3n + 3n

Combine like terms: -3n + 3n = 0
3n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '3n'.
3n(1 + 2n) = 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 '(1 + 2n)' equal to zero and attempt to solve:

Simplifying
1 + 2n = 0

Solving
1 + 2n = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2n = 0 + -1
2n = 0 + -1

Combine like terms: 0 + -1 = -1
2n = -1

Divide each side by '2'.
n = -0.5

Simplifying
n = -0.5
Solution
n = {0, -0.5}