-9n^2+6n+6=3

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

Simplifying
-9n2 + 6n + 6 = 3

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

Solving
6 + 6n + -9n2 = 3

Solving for variable 'n'.

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

Combine like terms: 6 + -3 = 3
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}