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

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

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

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

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

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

Combine like terms: 1v + 4v = 5v
(4 + 5v + v2) = 0

Solving
4 + 5v + v2 = 0

Solving for variable 'v'.

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

Subproblem 1
Set the factor '(4 + v)' equal to zero and attempt to solve:

Simplifying
4 + v = 0

Solving
4 + v = 0

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

Add '-4' to each side of the equation.
4 + -4 + v = 0 + -4

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

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

Simplifying
v = -4
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 = {-4, -1}