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

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

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

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

Multiply (4 + v) * (1 + 4v)
(4(1 + 4v) + v(1 + 4v)) = 0
((1 * 4 + 4v * 4) + v(1 + 4v)) = 0
((4 + 16v) + v(1 + 4v)) = 0
(4 + 16v + (1 * v + 4v * v)) = 0
(4 + 16v + (1v + 4v2)) = 0

Combine like terms: 16v + 1v = 17v
(4 + 17v + 4v2) = 0

Solving
4 + 17v + 4v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(4 + v)(1 + 4v) = 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 + 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 = {-4, -0.25}