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

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

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

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

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

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

Combine like terms: 6v + -1v = 5v
3(-1 + 5v + 6v2) = 0
(-1 * 3 + 5v * 3 + 6v2 * 3) = 0
(-3 + 15v + 18v2) = 0

Solving
-3 + 15v + 18v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 5v + 6v2) = 0

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

Ignore the factor 3.
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 '(1 + -6v)' equal to zero and attempt to solve:

Simplifying
1 + -6v = 0

Solving
1 + -6v = 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 + -6v = 0 + -1

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

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

Divide each side by '-6'.
v = 0.1666666667

Simplifying
v = 0.1666666667
Solution
v = {-1, 0.1666666667}