(9n^2)+6n=3

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

Simplifying
(9n2) + 6n = 3

Reorder the terms:
6n + (9n2) = 3

Solving
6n + (9n2) = 3

Solving for variable 'n'.

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

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

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

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

Simplifying
1 + -3n = 0

Solving
1 + -3n = 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 + -3n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3n = 0 + -1
-3n = 0 + -1

Combine like terms: 0 + -1 = -1
-3n = -1

Divide each side by '-3'.
n = 0.3333333333

Simplifying
n = 0.3333333333
Solution
n = {-1, 0.3333333333}