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

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

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

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

Multiply (3 + -1v) * (1 + 3v)
(3(1 + 3v) + -1v * (1 + 3v)) = 0
((1 * 3 + 3v * 3) + -1v * (1 + 3v)) = 0
((3 + 9v) + -1v * (1 + 3v)) = 0
(3 + 9v + (1 * -1v + 3v * -1v)) = 0
(3 + 9v + (-1v + -3v2)) = 0

Combine like terms: 9v + -1v = 8v
(3 + 8v + -3v2) = 0

Solving
3 + 8v + -3v2 = 0

Solving for variable 'v'.

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

Subproblem 1
Set the factor '(3 + -1v)' equal to zero and attempt to solve:

Simplifying
3 + -1v = 0

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

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

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

Divide each side by '-1'.
v = 3

Simplifying
v = 3
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 = {3, -0.3333333333}