(1[5v+3]1)(1[1-v]1)=0

Solution for (1[5v+3]1)(1[1-v]1)=0 equation:

Simplifying
(1[5v + 3] * 1)(1[1 + -1v] * 1) = 0

Reorder the terms:
(1[3 + 5v] * 1)(1[1 + -1v] * 1) = 0

Reorder the terms for easier multiplication:
(1 * 1[3 + 5v])(1[1 + -1v] * 1) = 0

Multiply 1 * 1
(1[3 + 5v])(1[1 + -1v] * 1) = 0
([3 * 1 + 5v * 1])(1[1 + -1v] * 1) = 0
([3 + 5v])(1[1 + -1v] * 1) = 0

Reorder the terms for easier multiplication:
(3 + 5v)(1 * 1[1 + -1v]) = 0

Multiply 1 * 1
(3 + 5v)(1[1 + -1v]) = 0
(3 + 5v)([1 * 1 + -1v * 1]) = 0
(3 + 5v)([1 + -1v]) = 0

Multiply (3 + 5v) * (1 + -1v)
(3(1 + -1v) + 5v * (1 + -1v)) = 0
((1 * 3 + -1v * 3) + 5v * (1 + -1v)) = 0
((3 + -3v) + 5v * (1 + -1v)) = 0
(3 + -3v + (1 * 5v + -1v * 5v)) = 0
(3 + -3v + (5v + -5v2)) = 0

Combine like terms: -3v + 5v = 2v
(3 + 2v + -5v2) = 0

Solving
3 + 2v + -5v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(1 + -1v)(3 + 5v) = 0

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

Simplifying
1 + -1v = 0

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

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

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

Divide each side by '-1'.
v = 1

Simplifying
v = 1
Subproblem 2
Set the factor '(3 + 5v)' equal to zero and attempt to solve:

Simplifying
3 + 5v = 0

Solving
3 + 5v = 0

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

Add '-3' to each side of the equation.
3 + -3 + 5v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5v = 0 + -3
5v = 0 + -3

Combine like terms: 0 + -3 = -3
5v = -3

Divide each side by '5'.
v = -0.6

Simplifying
v = -0.6
Solution
v = {1, -0.6}