8v^3=8v

Solution for 8v^3=8v equation:

Simplifying
8v3 = 8v

Solving
8v3 = 8v

Solving for variable 'v'.

Reorder the terms:
-8v + 8v3 = 8v + -8v

Combine like terms: 8v + -8v = 0
-8v + 8v3 = 0

Factor out the Greatest Common Factor (GCF), '8v'.
8v(-1 + v2) = 0

Factor a difference between two squares.
8v((1 + v)(-1 + v)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor 'v' equal to zero and attempt to solve:

Simplifying
v = 0

Solving
v = 0

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

Simplifying
v = 0
Subproblem 2
Set the factor '(1 + v)' equal to zero and attempt to solve:

Simplifying
1 + v = 0

Solving
1 + v = 0

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

Add '-1' to each side of the equation.
1 + -1 + v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + v = 0 + -1
v = 0 + -1

Combine like terms: 0 + -1 = -1
v = -1

Simplifying
v = -1
Subproblem 3
Set the factor '(-1 + v)' equal to zero and attempt to solve:

Simplifying
-1 + v = 0

Solving
-1 + v = 0

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

Add '1' to each side of the equation.
-1 + 1 + v = 0 + 1

Combine like terms: -1 + 1 = 0
0 + v = 0 + 1
v = 0 + 1

Combine like terms: 0 + 1 = 1
v = 1

Simplifying
v = 1
Solution
v = {0, -1, 1}