3z^4-48=

Solution for 3z^4-48= equation:

Simplifying
3z4 + -48 = 0

Reorder the terms:
-48 + 3z4 = 0

Solving
-48 + 3z4 = 0

Solving for variable 'z'.

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

Add '48' to each side of the equation.
-48 + 48 + 3z4 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 3z4 = 0 + 48
3z4 = 0 + 48

Combine like terms: 0 + 48 = 48
3z4 = 48

Divide each side by '3'.
z4 = 16

Simplifying
z4 = 16

Reorder the terms:
-16 + z4 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + z4 = 0

Factor a difference between two squares.
(4 + z2)(-4 + z2) = 0

Factor a difference between two squares.
(4 + z2)((2 + z)(-2 + z)) = 0

Subproblem 1
Set the factor '(4 + z2)' equal to zero and attempt to solve:

Simplifying
4 + z2 = 0

Solving
4 + z2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + z2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + z2 = 0 + -4
z2 = 0 + -4

Combine like terms: 0 + -4 = -4
z2 = -4

Simplifying
z2 = -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 + z)' equal to zero and attempt to solve:

Simplifying
2 + z = 0

Solving
2 + z = 0

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

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

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

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

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

Simplifying
-2 + z = 0

Solving
-2 + z = 0

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

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

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

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

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