4m^8-53m^4+49=

Solution for 4m^8-53m^4+49= equation:

Simplifying
4m8 + -53m4 + 49 = 0

Reorder the terms:
49 + -53m4 + 4m8 = 0

Solving
49 + -53m4 + 4m8 = 0

Solving for variable 'm'.

Factor a trinomial.
(1 + -1m4)(49 + -4m4) = 0

Factor a difference between two squares.
((1 + m2)(1 + -1m2))(49 + -4m4) = 0

Factor a difference between two squares.
((1 + m2)((1 + m)(1 + -1m)))(49 + -4m4) = 0

Factor a difference between two squares.
((7 + 2m2)(7 + -2m2))(1 + m2)(1 + m)(1 + -1m) = 0

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

Simplifying
1 + m2 = 0

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

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

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

Simplifying
m2 = -1

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
Subproblem 4
Set the factor '(7 + 2m2)' equal to zero and attempt to solve:

Simplifying
7 + 2m2 = 0

Solving
7 + 2m2 = 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 + 2m2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2m2 = 0 + -7
2m2 = 0 + -7

Combine like terms: 0 + -7 = -7
2m2 = -7

Divide each side by '2'.
m2 = -3.5

Simplifying
m2 = -3.5

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 5
Set the factor '(7 + -2m2)' equal to zero and attempt to solve:

Simplifying
7 + -2m2 = 0

Solving
7 + -2m2 = 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 + -2m2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2m2 = 0 + -7
-2m2 = 0 + -7

Combine like terms: 0 + -7 = -7
-2m2 = -7

Divide each side by '-2'.
m2 = 3.5

Simplifying
m2 = 3.5

Take the square root of each side:
m = {-1.870828693, 1.870828693}
Solution
m = {-1, 1, -1.870828693, 1.870828693}