(1[4v+2]1)(1[4+v]1)=0

Solution for (1[4v+2]1)(1[4+v]1)=0 equation:

Simplifying
(1[4v + 2] * 1)(1[4 + v] * 1) = 0

Reorder the terms:
(1[2 + 4v] * 1)(1[4 + v] * 1) = 0

Reorder the terms for easier multiplication:
(1 * 1[2 + 4v])(1[4 + v] * 1) = 0

Multiply 1 * 1
(1[2 + 4v])(1[4 + v] * 1) = 0
([2 * 1 + 4v * 1])(1[4 + v] * 1) = 0
([2 + 4v])(1[4 + v] * 1) = 0

Reorder the terms for easier multiplication:
(2 + 4v)(1 * 1[4 + v]) = 0

Multiply 1 * 1
(2 + 4v)(1[4 + v]) = 0
(2 + 4v)([4 * 1 + v * 1]) = 0
(2 + 4v)([4 + 1v]) = 0

Multiply (2 + 4v) * (4 + 1v)
(2(4 + 1v) + 4v * (4 + 1v)) = 0
((4 * 2 + 1v * 2) + 4v * (4 + 1v)) = 0
((8 + 2v) + 4v * (4 + 1v)) = 0
(8 + 2v + (4 * 4v + 1v * 4v)) = 0
(8 + 2v + (16v + 4v2)) = 0

Combine like terms: 2v + 16v = 18v
(8 + 18v + 4v2) = 0

Solving
8 + 18v + 4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 9v + 2v2) = 0

Factor a trinomial.
2((4 + v)(1 + 2v)) = 0

Ignore the factor 2.
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 + 2v)' equal to zero and attempt to solve:

Simplifying
1 + 2v = 0

Solving
1 + 2v = 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 + 2v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2v = 0 + -1
2v = 0 + -1

Combine like terms: 0 + -1 = -1
2v = -1

Divide each side by '2'.
v = -0.5

Simplifying
v = -0.5
Solution
v = {-4, -0.5}