3(v+5)(-v+4)=0

Solution for 3(v+5)(-v+4)=0 equation:

Simplifying
3(v + 5)(-1v + 4) = 0

Reorder the terms:
3(5 + v)(-1v + 4) = 0

Reorder the terms:
3(5 + v)(4 + -1v) = 0

Multiply (5 + v) * (4 + -1v)
3(5(4 + -1v) + v(4 + -1v)) = 0
3((4 * 5 + -1v * 5) + v(4 + -1v)) = 0
3((20 + -5v) + v(4 + -1v)) = 0
3(20 + -5v + (4 * v + -1v * v)) = 0
3(20 + -5v + (4v + -1v2)) = 0

Combine like terms: -5v + 4v = -1v
3(20 + -1v + -1v2) = 0
(20 * 3 + -1v * 3 + -1v2 * 3) = 0
(60 + -3v + -3v2) = 0

Solving
60 + -3v + -3v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '3'.
3(20 + -1v + -1v2) = 0

Factor a trinomial.
3((4 + -1v)(5 + v)) = 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 '(5 + v)' equal to zero and attempt to solve:

Simplifying
5 + v = 0

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

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

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

Simplifying
v = -5
Solution
v = {4, -5}