3m^4-243=0

Solution for 3m^4-243=0 equation:

Simplifying
3m4 + -243 = 0

Reorder the terms:
-243 + 3m4 = 0

Solving
-243 + 3m4 = 0

Solving for variable 'm'.

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

Add '243' to each side of the equation.
-243 + 243 + 3m4 = 0 + 243

Combine like terms: -243 + 243 = 0
0 + 3m4 = 0 + 243
3m4 = 0 + 243

Combine like terms: 0 + 243 = 243
3m4 = 243

Divide each side by '3'.
m4 = 81

Simplifying
m4 = 81

Reorder the terms:
-81 + m4 = 81 + -81

Combine like terms: 81 + -81 = 0
-81 + m4 = 0

Factor a difference between two squares.
(9 + m2)(-9 + m2) = 0

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

Subproblem 1
Set the factor '(9 + m2)' equal to zero and attempt to solve:

Simplifying
9 + m2 = 0

Solving
9 + m2 = 0

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

Add '-9' to each side of the equation.
9 + -9 + m2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + m2 = 0 + -9
m2 = 0 + -9

Combine like terms: 0 + -9 = -9
m2 = -9

Simplifying
m2 = -9

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 '(3 + m)' equal to zero and attempt to solve:

Simplifying
3 + m = 0

Solving
3 + m = 0

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

Add '-3' to each side of the equation.
3 + -3 + m = 0 + -3

Combine like terms: 3 + -3 = 0
0 + m = 0 + -3
m = 0 + -3

Combine like terms: 0 + -3 = -3
m = -3

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

Simplifying
-3 + m = 0

Solving
-3 + m = 0

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

Add '3' to each side of the equation.
-3 + 3 + m = 0 + 3

Combine like terms: -3 + 3 = 0
0 + m = 0 + 3
m = 0 + 3

Combine like terms: 0 + 3 = 3
m = 3

Simplifying
m = 3
Solution
m = {-3, 3}