41n^2+40n-1=0

Solution for 41n^2+40n-1=0 equation:

Simplifying
41n2 + 40n + -1 = 0

Reorder the terms:
-1 + 40n + 41n2 = 0

Solving
-1 + 40n + 41n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1 + -1n)(1 + -41n) = 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 + -41n)' equal to zero and attempt to solve:

Simplifying
1 + -41n = 0

Solving
1 + -41n = 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 + -41n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -41n = 0 + -1
-41n = 0 + -1

Combine like terms: 0 + -1 = -1
-41n = -1

Divide each side by '-41'.
n = 0.0243902439

Simplifying
n = 0.0243902439
Solution
n = {-1, 0.0243902439}