3(v+8)(-v-6)=0

Solution for 3(v+8)(-v-6)=0 equation:

Simplifying
3(v + 8)(-1v + -6) = 0

Reorder the terms:
3(8 + v)(-1v + -6) = 0

Reorder the terms:
3(8 + v)(-6 + -1v) = 0

Multiply (8 + v) * (-6 + -1v)
3(8(-6 + -1v) + v(-6 + -1v)) = 0
3((-6 * 8 + -1v * 8) + v(-6 + -1v)) = 0
3((-48 + -8v) + v(-6 + -1v)) = 0
3(-48 + -8v + (-6 * v + -1v * v)) = 0
3(-48 + -8v + (-6v + -1v2)) = 0

Combine like terms: -8v + -6v = -14v
3(-48 + -14v + -1v2) = 0
(-48 * 3 + -14v * 3 + -1v2 * 3) = 0
(-144 + -42v + -3v2) = 0

Solving
-144 + -42v + -3v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '-3'.
-3(48 + 14v + v2) = 0

Factor a trinomial.
-3((8 + v)(6 + v)) = 0

Ignore the factor -3.
Subproblem 1
Set the factor '(8 + v)' equal to zero and attempt to solve:

Simplifying
8 + v = 0

Solving
8 + v = 0

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

Add '-8' to each side of the equation.
8 + -8 + v = 0 + -8

Combine like terms: 8 + -8 = 0
0 + v = 0 + -8
v = 0 + -8

Combine like terms: 0 + -8 = -8
v = -8

Simplifying
v = -8
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 = {-8, -6}