4v^2+v=0

Solution for 4v^2+v=0 equation:

Simplifying
4v2 + v = 0

Reorder the terms:
v + 4v2 = 0

Solving
v + 4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), 'v'.
v(1 + 4v) = 0

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 + 4v)' equal to zero and attempt to solve:

Simplifying
1 + 4v = 0

Solving
1 + 4v = 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 + 4v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4v = 0 + -1
4v = 0 + -1

Combine like terms: 0 + -1 = -1
4v = -1

Divide each side by '4'.
v = -0.25

Simplifying
v = -0.25
Solution
v = {0, -0.25}