41M^2+40M-1=0

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

Simplifying
41M2 + 40M + -1 = 0

Reorder the terms:
-1 + 40M + 41M2 = 0

Solving
-1 + 40M + 41M2 = 0

Solving for variable 'M'.

Factor a trinomial.
(-1 + -1M)(1 + -41M) = 0

Subproblem 1
Set the factor '(-1 + -1M)' equal to zero and attempt to solve:

Simplifying
-1 + -1M = 0

Solving
-1 + -1M = 0

Move all terms containing M to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -1M = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1M = 0 + 1
-1M = 0 + 1

Combine like terms: 0 + 1 = 1
-1M = 1

Divide each side by '-1'.
M = -1

Simplifying
M = -1
Subproblem 2
Set the factor '(1 + -41M)' equal to zero and attempt to solve:

Simplifying
1 + -41M = 0

Solving
1 + -41M = 0

Move all terms containing M to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -41M = 0 + -1

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

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

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

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