3q^4-48=0

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

Simplifying
3q4 + -48 = 0

Reorder the terms:
-48 + 3q4 = 0

Solving
-48 + 3q4 = 0

Solving for variable 'q'.

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

Add '48' to each side of the equation.
-48 + 48 + 3q4 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 3q4 = 0 + 48
3q4 = 0 + 48

Combine like terms: 0 + 48 = 48
3q4 = 48

Divide each side by '3'.
q4 = 16

Simplifying
q4 = 16

Reorder the terms:
-16 + q4 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + q4 = 0

Factor a difference between two squares.
(4 + q2)(-4 + q2) = 0

Factor a difference between two squares.
(4 + q2)((2 + q)(-2 + q)) = 0

Subproblem 1
Set the factor '(4 + q2)' equal to zero and attempt to solve:

Simplifying
4 + q2 = 0

Solving
4 + q2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + q2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + q2 = 0 + -4
q2 = 0 + -4

Combine like terms: 0 + -4 = -4
q2 = -4

Simplifying
q2 = -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 + q)' equal to zero and attempt to solve:

Simplifying
2 + q = 0

Solving
2 + q = 0

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

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

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

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

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

Simplifying
-2 + q = 0

Solving
-2 + q = 0

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

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

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

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

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