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

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

Simplifying
(5 + -1v)(3v + 1) = 0

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

Multiply (5 + -1v) * (1 + 3v)
(5(1 + 3v) + -1v * (1 + 3v)) = 0
((1 * 5 + 3v * 5) + -1v * (1 + 3v)) = 0
((5 + 15v) + -1v * (1 + 3v)) = 0
(5 + 15v + (1 * -1v + 3v * -1v)) = 0
(5 + 15v + (-1v + -3v2)) = 0

Combine like terms: 15v + -1v = 14v
(5 + 14v + -3v2) = 0

Solving
5 + 14v + -3v2 = 0

Solving for variable 'v'.

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

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

Simplifying
5 + -1v = 0

Solving
5 + -1v = 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 + -1v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1v = 0 + -5
-1v = 0 + -5

Combine like terms: 0 + -5 = -5
-1v = -5

Divide each side by '-1'.
v = 5

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

Simplifying
1 + 3v = 0

Solving
1 + 3v = 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 + 3v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3v = 0 + -1
3v = 0 + -1

Combine like terms: 0 + -1 = -1
3v = -1

Divide each side by '3'.
v = -0.3333333333

Simplifying
v = -0.3333333333
Solution
v = {5, -0.3333333333}