25m^4-41m^2+16=0

Solution for 25m^4-41m^2+16=0 equation:

Simplifying
25m4 + -41m2 + 16 = 0

Reorder the terms:
16 + -41m2 + 25m4 = 0

Solving
16 + -41m2 + 25m4 = 0

Solving for variable 'm'.

Factor a trinomial.
(16 + -25m2)(1 + -1m2) = 0

Factor a difference between two squares.
((4 + 5m)(4 + -5m))(1 + -1m2) = 0

Factor a difference between two squares.
((1 + m)(1 + -1m))(4 + 5m)(4 + -5m) = 0

Subproblem 1
Set the factor '(4 + 5m)' equal to zero and attempt to solve:

Simplifying
4 + 5m = 0

Solving
4 + 5m = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5m = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5m = 0 + -4
5m = 0 + -4

Combine like terms: 0 + -4 = -4
5m = -4

Divide each side by '5'.
m = -0.8

Simplifying
m = -0.8
Subproblem 2
Set the factor '(4 + -5m)' equal to zero and attempt to solve:

Simplifying
4 + -5m = 0

Solving
4 + -5m = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5m = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5m = 0 + -4
-5m = 0 + -4

Combine like terms: 0 + -4 = -4
-5m = -4

Divide each side by '-5'.
m = 0.8

Simplifying
m = 0.8
Subproblem 3
Set the factor '(1 + m)' equal to zero and attempt to solve:

Simplifying
1 + m = 0

Solving
1 + m = 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 + m = 0 + -1

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

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

Simplifying
m = -1
Subproblem 4
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
Solution
m = {-0.8, 0.8, -1, 1}