3m^2-48m^6=0

Solution for 3m^2-48m^6=0 equation:

Simplifying
3m2 + -48m6 = 0

Solving
3m2 + -48m6 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '3m2'.
3m2(1 + -16m4) = 0

Factor a difference between two squares.
3m2((1 + 4m2)(1 + -4m2)) = 0

Factor a difference between two squares.
3m2((1 + 4m2)((1 + 2m)(1 + -2m))) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'm2' equal to zero and attempt to solve:

Simplifying
m2 = 0

Solving
m2 = 0

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

Simplifying
m2 = 0

Take the square root of each side:
m = {0}
Subproblem 2
Set the factor '(1 + 4m2)' equal to zero and attempt to solve:

Simplifying
1 + 4m2 = 0

Solving
1 + 4m2 = 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 + 4m2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4m2 = 0 + -1
4m2 = 0 + -1

Combine like terms: 0 + -1 = -1
4m2 = -1

Divide each side by '4'.
m2 = -0.25

Simplifying
m2 = -0.25

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(1 + 2m)' equal to zero and attempt to solve:

Simplifying
1 + 2m = 0

Solving
1 + 2m = 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 + 2m = 0 + -1

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

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

Divide each side by '2'.
m = -0.5

Simplifying
m = -0.5
Subproblem 4
Set the factor '(1 + -2m)' equal to zero and attempt to solve:

Simplifying
1 + -2m = 0

Solving
1 + -2m = 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 + -2m = 0 + -1

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

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

Divide each side by '-2'.
m = 0.5

Simplifying
m = 0.5
Solution
m = {0, -0.5, 0.5}