m^4-38m^2+72=

Solution for m^4-38m^2+72= equation:

Simplifying
m4 + -38m2 + 72 = 0

Reorder the terms:
72 + -38m2 + m4 = 0

Solving
72 + -38m2 + m4 = 0

Solving for variable 'm'.

Factor a trinomial.
(2 + -1m2)(36 + -1m2) = 0

Factor a difference between two squares.
(2 + -1m2)((6 + m)(6 + -1m)) = 0

Subproblem 1
Set the factor '(2 + -1m2)' equal to zero and attempt to solve:

Simplifying
2 + -1m2 = 0

Solving
2 + -1m2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1m2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1m2 = 0 + -2
-1m2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1m2 = -2

Divide each side by '-1'.
m2 = 2

Simplifying
m2 = 2

Take the square root of each side:
m = {-1.414213562, 1.414213562}
Subproblem 2
Set the factor '(6 + m)' equal to zero and attempt to solve:

Simplifying
6 + m = 0

Solving
6 + m = 0

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

Add '-6' to each side of the equation.
6 + -6 + m = 0 + -6

Combine like terms: 6 + -6 = 0
0 + m = 0 + -6
m = 0 + -6

Combine like terms: 0 + -6 = -6
m = -6

Simplifying
m = -6
Subproblem 3
Set the factor '(6 + -1m)' equal to zero and attempt to solve:

Simplifying
6 + -1m = 0

Solving
6 + -1m = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1m = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1m = 0 + -6
-1m = 0 + -6

Combine like terms: 0 + -6 = -6
-1m = -6

Divide each side by '-1'.
m = 6

Simplifying
m = 6
Solution
m = {-1.414213562, 1.414213562, -6, 6}