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

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

Simplifying
m4 + 6m2 + -7 = 0

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

Solving
-7 + 6m2 + m4 = 0

Solving for variable 'm'.

Factor a trinomial.
(-7 + -1m2)(1 + -1m2) = 0

Factor a difference between two squares.
(-7 + -1m2)((1 + m)(1 + -1m)) = 0

Subproblem 1
Set the factor '(-7 + -1m2)' equal to zero and attempt to solve:

Simplifying
-7 + -1m2 = 0

Solving
-7 + -1m2 = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1m2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1m2 = 0 + 7
-1m2 = 0 + 7

Combine like terms: 0 + 7 = 7
-1m2 = 7

Divide each side by '-1'.
m2 = -7

Simplifying
m2 = -7

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
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 = {-1, 1}