4v(v+6)(v-1)=0

Solution for 4v(v+6)(v-1)=0 equation:

Simplifying
4v(v + 6)(v + -1) = 0

Reorder the terms:
4v(6 + v)(v + -1) = 0

Reorder the terms:
4v(6 + v)(-1 + v) = 0

Multiply (6 + v) * (-1 + v)
4v(6(-1 + v) + v(-1 + v)) = 0
4v((-1 * 6 + v * 6) + v(-1 + v)) = 0
4v((-6 + 6v) + v(-1 + v)) = 0
4v(-6 + 6v + (-1 * v + v * v)) = 0
4v(-6 + 6v + (-1v + v2)) = 0

Combine like terms: 6v + -1v = 5v
4v(-6 + 5v + v2) = 0
(-6 * 4v + 5v * 4v + v2 * 4v) = 0
(-24v + 20v2 + 4v3) = 0

Solving
-24v + 20v2 + 4v3 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '4v'.
4v(-6 + 5v + v2) = 0

Factor a trinomial.
4v((-6 + -1v)(1 + -1v)) = 0

Ignore the factor 4.
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 '(-6 + -1v)' equal to zero and attempt to solve:

Simplifying
-6 + -1v = 0

Solving
-6 + -1v = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1v = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1v = 0 + 6
-1v = 0 + 6

Combine like terms: 0 + 6 = 6
-1v = 6

Divide each side by '-1'.
v = -6

Simplifying
v = -6
Subproblem 3
Set the factor '(1 + -1v)' equal to zero and attempt to solve:

Simplifying
1 + -1v = 0

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

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

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

Divide each side by '-1'.
v = 1

Simplifying
v = 1
Solution
v = {0, -6, 1}