(v+5)(v+1)=0

Solution for (v+5)(v+1)=0 equation:

Simplifying
(v + 5)(v + 1) = 0

Reorder the terms:
(5 + v)(v + 1) = 0

Reorder the terms:
(5 + v)(1 + v) = 0

Multiply (5 + v) * (1 + v)
(5(1 + v) + v(1 + v)) = 0
((1 * 5 + v * 5) + v(1 + v)) = 0
((5 + 5v) + v(1 + v)) = 0
(5 + 5v + (1 * v + v * v)) = 0
(5 + 5v + (1v + v2)) = 0

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

Solving
5 + 6v + v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(5 + v)(1 + v) = 0

Subproblem 1
Set the factor '(5 + v)' equal to zero and attempt to solve:

Simplifying
5 + v = 0

Solving
5 + v = 0

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

Add '-5' to each side of the equation.
5 + -5 + v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + v = 0 + -5
v = 0 + -5

Combine like terms: 0 + -5 = -5
v = -5

Simplifying
v = -5
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
Solution
v = {-5, -1}