16x^3-v^4x^3=0

Solution for 16x^3-v^4x^3=0 equation:

Simplifying
16x3 + -1v4x3 = 0

Reorder the terms:
-1v4x3 + 16x3 = 0

Solving
-1v4x3 + 16x3 = 0

Solving for variable 'v'.

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

Add '-16x3' to each side of the equation.
-1v4x3 + 16x3 + -16x3 = 0 + -16x3

Combine like terms: 16x3 + -16x3 = 0
-1v4x3 + 0 = 0 + -16x3
-1v4x3 = 0 + -16x3
Remove the zero:
-1v4x3 = -16x3

Divide each side by '-1x3'.
v4 = 16

Simplifying
v4 = 16

Reorder the terms:
-16 + v4 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + v4 = 0

Factor a difference between two squares.
(4 + v2)(-4 + v2) = 0

Factor a difference between two squares.
(4 + v2)((2 + v)(-2 + v)) = 0

Subproblem 1
Set the factor '(4 + v2)' equal to zero and attempt to solve:

Simplifying
4 + v2 = 0

Solving
4 + v2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + v2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + v2 = 0 + -4
v2 = 0 + -4

Combine like terms: 0 + -4 = -4
v2 = -4

Simplifying
v2 = -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 + v)' equal to zero and attempt to solve:

Simplifying
2 + v = 0

Solving
2 + v = 0

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

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

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

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

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

Simplifying
-2 + v = 0

Solving
-2 + v = 0

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

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

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

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

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