-9n^2+8n+1=0

Solution for -9n^2+8n+1=0 equation:

Simplifying
-9n2 + 8n + 1 = 0

Reorder the terms:
1 + 8n + -9n2 = 0

Solving
1 + 8n + -9n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(1 + -1n)(1 + 9n) = 0

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 + 9n)' equal to zero and attempt to solve:

Simplifying
1 + 9n = 0

Solving
1 + 9n = 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 + 9n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 9n = 0 + -1
9n = 0 + -1

Combine like terms: 0 + -1 = -1
9n = -1

Divide each side by '9'.
n = -0.1111111111

Simplifying
n = -0.1111111111
Solution
n = {1, -0.1111111111}