(3v+1)(6-v)=0

Solution for (3v+1)(6-v)=0 equation:

Simplifying
(3v + 1)(6 + -1v) = 0

Reorder the terms:
(1 + 3v)(6 + -1v) = 0

Multiply (1 + 3v) * (6 + -1v)
(1(6 + -1v) + 3v * (6 + -1v)) = 0
((6 * 1 + -1v * 1) + 3v * (6 + -1v)) = 0
((6 + -1v) + 3v * (6 + -1v)) = 0
(6 + -1v + (6 * 3v + -1v * 3v)) = 0
(6 + -1v + (18v + -3v2)) = 0

Combine like terms: -1v + 18v = 17v
(6 + 17v + -3v2) = 0

Solving
6 + 17v + -3v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(6 + -1v)(1 + 3v) = 0

Subproblem 1
Set the factor '(6 + -1v)' equal to zero and attempt to solve:

Simplifying
6 + -1v = 0

Solving
6 + -1v = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1v = 0 + -6
-1v = 0 + -6

Combine like terms: 0 + -6 = -6
-1v = -6

Divide each side by '-1'.
v = 6

Simplifying
v = 6
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 = {6, -0.3333333333}