3(3v-1)(v+4)=0

Solution for 3(3v-1)(v+4)=0 equation:

Simplifying
3(3v + -1)(v + 4) = 0

Reorder the terms:
3(-1 + 3v)(v + 4) = 0

Reorder the terms:
3(-1 + 3v)(4 + v) = 0

Multiply (-1 + 3v) * (4 + v)
3(-1(4 + v) + 3v * (4 + v)) = 0
3((4 * -1 + v * -1) + 3v * (4 + v)) = 0
3((-4 + -1v) + 3v * (4 + v)) = 0
3(-4 + -1v + (4 * 3v + v * 3v)) = 0
3(-4 + -1v + (12v + 3v2)) = 0

Combine like terms: -1v + 12v = 11v
3(-4 + 11v + 3v2) = 0
(-4 * 3 + 11v * 3 + 3v2 * 3) = 0
(-12 + 33v + 9v2) = 0

Solving
-12 + 33v + 9v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 11v + 3v2) = 0

Factor a trinomial.
3((-4 + -1v)(1 + -3v)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -1v)' equal to zero and attempt to solve:

Simplifying
-4 + -1v = 0

Solving
-4 + -1v = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1v = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1v = 0 + 4
-1v = 0 + 4

Combine like terms: 0 + 4 = 4
-1v = 4

Divide each side by '-1'.
v = -4

Simplifying
v = -4
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 = {-4, 0.3333333333}