m^4-21m^2+80=0

Solution for m^4-21m^2+80=0 equation:

Simplifying
m4 + -21m2 + 80 = 0

Reorder the terms:
80 + -21m2 + m4 = 0

Solving
80 + -21m2 + m4 = 0

Solving for variable 'm'.

Factor a trinomial.
(5 + -1m2)(16 + -1m2) = 0

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

Subproblem 1
Set the factor '(5 + -1m2)' equal to zero and attempt to solve:

Simplifying
5 + -1m2 = 0

Solving
5 + -1m2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1m2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1m2 = 0 + -5
-1m2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1m2 = -5

Divide each side by '-1'.
m2 = 5

Simplifying
m2 = 5

Take the square root of each side:
m = {-2.236067978, 2.236067978}
Subproblem 2
Set the factor '(4 + m)' equal to zero and attempt to solve:

Simplifying
4 + m = 0

Solving
4 + m = 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 + m = 0 + -4

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

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

Simplifying
m = -4
Subproblem 3
Set the factor '(4 + -1m)' equal to zero and attempt to solve:

Simplifying
4 + -1m = 0

Solving
4 + -1m = 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 + -1m = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1m = 0 + -4
-1m = 0 + -4

Combine like terms: 0 + -4 = -4
-1m = -4

Divide each side by '-1'.
m = 4

Simplifying
m = 4
Solution
m = {-2.236067978, 2.236067978, -4, 4}