6n^2=-3-9n

Solution for 6n^2=-3-9n equation:

Simplifying
6n2 = -3 + -9n

Solving
6n2 = -3 + -9n

Solving for variable 'n'.

Reorder the terms:
3 + 9n + 6n2 = -3 + -9n + 3 + 9n

Reorder the terms:
3 + 9n + 6n2 = -3 + 3 + -9n + 9n

Combine like terms: -3 + 3 = 0
3 + 9n + 6n2 = 0 + -9n + 9n
3 + 9n + 6n2 = -9n + 9n

Combine like terms: -9n + 9n = 0
3 + 9n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 3n + 2n2) = 0

Factor a trinomial.
3((1 + n)(1 + 2n)) = 0

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

Simplifying
1 + n = 0

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

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

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

Simplifying
n = -1
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 = {-1, -0.5}