3w^4-48=0

Solution for 3w^4-48=0 equation:

Simplifying
3w4 + -48 = 0

Reorder the terms:
-48 + 3w4 = 0

Solving
-48 + 3w4 = 0

Solving for variable 'w'.

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

Add '48' to each side of the equation.
-48 + 48 + 3w4 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 3w4 = 0 + 48
3w4 = 0 + 48

Combine like terms: 0 + 48 = 48
3w4 = 48

Divide each side by '3'.
w4 = 16

Simplifying
w4 = 16

Reorder the terms:
-16 + w4 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + w4 = 0

Factor a difference between two squares.
(4 + w2)(-4 + w2) = 0

Factor a difference between two squares.
(4 + w2)((2 + w)(-2 + w)) = 0

Subproblem 1
Set the factor '(4 + w2)' equal to zero and attempt to solve:

Simplifying
4 + w2 = 0

Solving
4 + w2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + w2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + w2 = 0 + -4
w2 = 0 + -4

Combine like terms: 0 + -4 = -4
w2 = -4

Simplifying
w2 = -4

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 '(2 + w)' equal to zero and attempt to solve:

Simplifying
2 + w = 0

Solving
2 + w = 0

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

Add '-2' to each side of the equation.
2 + -2 + w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + w = 0 + -2
w = 0 + -2

Combine like terms: 0 + -2 = -2
w = -2

Simplifying
w = -2
Subproblem 3
Set the factor '(-2 + w)' equal to zero and attempt to solve:

Simplifying
-2 + w = 0

Solving
-2 + w = 0

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

Add '2' to each side of the equation.
-2 + 2 + w = 0 + 2

Combine like terms: -2 + 2 = 0
0 + w = 0 + 2
w = 0 + 2

Combine like terms: 0 + 2 = 2
w = 2

Simplifying
w = 2
Solution
w = {-2, 2}