-9n^2+6n+6=7

Solution for -9n^2+6n+6=7 equation:

Simplifying
-9n2 + 6n + 6 = 7

Reorder the terms:
6 + 6n + -9n2 = 7

Solving
6 + 6n + -9n2 = 7

Solving for variable 'n'.

Reorder the terms:
6 + -7 + 6n + -9n2 = 7 + -7

Combine like terms: 6 + -7 = -1
-1 + 6n + -9n2 = 7 + -7

Combine like terms: 7 + -7 = 0
-1 + 6n + -9n2 = 0

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

Subproblem 1
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
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 = {0.3333333333, 0.3333333333}