7v^3+v^2=0

Solution for 7v^3+v^2=0 equation:

Simplifying
7v3 + v2 = 0

Reorder the terms:
v2 + 7v3 = 0

Solving
v2 + 7v3 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), 'v2'.
v2(1 + 7v) = 0

Subproblem 1
Set the factor 'v2' equal to zero and attempt to solve:

Simplifying
v2 = 0

Solving
v2 = 0

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

Simplifying
v2 = 0

Take the square root of each side:
v = {0}
Subproblem 2
Set the factor '(1 + 7v)' equal to zero and attempt to solve:

Simplifying
1 + 7v = 0

Solving
1 + 7v = 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 + 7v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7v = 0 + -1
7v = 0 + -1

Combine like terms: 0 + -1 = -1
7v = -1

Divide each side by '7'.
v = -0.1428571429

Simplifying
v = -0.1428571429
Solution
v = {0, -0.1428571429}