3(v+4)(-v+2)=0

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Solution for 3(v+4)(-v+2)=0 equation: 


Simplifying
3(v + 4)(-1v + 2) = 0

Reorder the terms:
3(4 + v)(-1v + 2) = 0

Reorder the terms:
3(4 + v)(2 + -1v) = 0

Multiply (4 + v) * (2 + -1v)
3(4(2 + -1v) + v(2 + -1v)) = 0
3((2 * 4 + -1v * 4) + v(2 + -1v)) = 0
3((8 + -4v) + v(2 + -1v)) = 0
3(8 + -4v + (2 * v + -1v * v)) = 0
3(8 + -4v + (2v + -1v2)) = 0

Combine like terms: -4v + 2v = -2v
3(8 + -2v + -1v2) = 0
(8 * 3 + -2v * 3 + -1v2 * 3) = 0
(24 + -6v + -3v2) = 0

Solving
24 + -6v + -3v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + -2v + -1v2) = 0

Factor a trinomial.
3((2 + -1v)(4 + v)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(2 + -1v)' equal to zero and attempt to solve:

Simplifying
2 + -1v = 0

Solving
2 + -1v = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1v = 0 + -2
-1v = 0 + -2

Combine like terms: 0 + -2 = -2
-1v = -2

Divide each side by '-1'.
v = 2

Simplifying
v = 2

Subproblem 2
Set the factor '(4 + v)' equal to zero and attempt to solve:

Simplifying
4 + v = 0

Solving
4 + v = 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 + v = 0 + -4

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

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

Simplifying
v = -4
Solution
v = {2, -4}

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