4(v+6)(-v+5)=0

Solution for 4(v+6)(-v+5)=0 equation:

Simplifying
4(v + 6)(-1v + 5) = 0

Reorder the terms:
4(6 + v)(-1v + 5) = 0

Reorder the terms:
4(6 + v)(5 + -1v) = 0

Multiply (6 + v) * (5 + -1v)
4(6(5 + -1v) + v(5 + -1v)) = 0
4((5 * 6 + -1v * 6) + v(5 + -1v)) = 0
4((30 + -6v) + v(5 + -1v)) = 0
4(30 + -6v + (5 * v + -1v * v)) = 0
4(30 + -6v + (5v + -1v2)) = 0

Combine like terms: -6v + 5v = -1v
4(30 + -1v + -1v2) = 0
(30 * 4 + -1v * 4 + -1v2 * 4) = 0
(120 + -4v + -4v2) = 0

Solving
120 + -4v + -4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '4'.
4(30 + -1v + -1v2) = 0

Factor a trinomial.
4((5 + -1v)(6 + v)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(5 + -1v)' equal to zero and attempt to solve:

Simplifying
5 + -1v = 0

Solving
5 + -1v = 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 + -1v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1v = 0 + -5
-1v = 0 + -5

Combine like terms: 0 + -5 = -5
-1v = -5

Divide each side by '-1'.
v = 5

Simplifying
v = 5
Subproblem 2
Set the factor '(6 + v)' equal to zero and attempt to solve:

Simplifying
6 + v = 0

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

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

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

Simplifying
v = -6
Solution
v = {5, -6}