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

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

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

Reorder the terms for easier multiplication:
v(6 + -1v)(1 + v) = 0

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

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

Solving
6v + 5v2 + -1v3 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), 'v'.
v(6 + 5v + -1v2) = 0

Factor a trinomial.
v((6 + -1v)(1 + v)) = 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 '(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 + 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, 6, -1}