9n^2+3n=6

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

Simplifying
9n2 + 3n = 6

Reorder the terms:
3n + 9n2 = 6

Solving
3n + 9n2 = 6

Solving for variable 'n'.

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

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

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

Factor a trinomial.
3((-1 + -1n)(2 + -3n)) = 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 + -3n)' equal to zero and attempt to solve:

Simplifying
2 + -3n = 0

Solving
2 + -3n = 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 + -3n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3n = 0 + -2
-3n = 0 + -2

Combine like terms: 0 + -2 = -2
-3n = -2

Divide each side by '-3'.
n = 0.6666666667

Simplifying
n = 0.6666666667
Solution
n = {-1, 0.6666666667}