3n^2=-6+9n

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

Simplifying
3n2 = -6 + 9n

Solving
3n2 = -6 + 9n

Solving for variable 'n'.

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

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

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

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

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

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

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

Simplifying
1 + -1n = 0

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

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

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

Divide each side by '-1'.
n = 1

Simplifying
n = 1
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

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

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

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

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {1, 2}