m^4-7m^2+6=0

Solution for m^4-7m^2+6=0 equation:

Simplifying
m4 + -7m2 + 6 = 0

Reorder the terms:
6 + -7m2 + m4 = 0

Solving
6 + -7m2 + m4 = 0

Solving for variable 'm'.

Factor a trinomial.
(1 + -1m2)(6 + -1m2) = 0

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

Subproblem 1
Set the factor '(6 + -1m2)' equal to zero and attempt to solve:

Simplifying
6 + -1m2 = 0

Solving
6 + -1m2 = 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 + -1m2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1m2 = 0 + -6
-1m2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1m2 = -6

Divide each side by '-1'.
m2 = 6

Simplifying
m2 = 6

Take the square root of each side:
m = {-2.449489743, 2.449489743}
Subproblem 2
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 3
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 = {-2.449489743, 2.449489743, -1, 1}