(4v-4w)(3v+9w)=0

Solution for (4v-4w)(3v+9w)=0 equation:

Simplifying
(4v + -4w)(3v + 9w) = 0

Multiply (4v + -4w) * (3v + 9w)
(4v * (3v + 9w) + -4w * (3v + 9w)) = 0
((3v * 4v + 9w * 4v) + -4w * (3v + 9w)) = 0

Reorder the terms:
((36vw + 12v2) + -4w * (3v + 9w)) = 0
((36vw + 12v2) + -4w * (3v + 9w)) = 0
(36vw + 12v2 + (3v * -4w + 9w * -4w)) = 0
(36vw + 12v2 + (-12vw + -36w2)) = 0

Reorder the terms:
(36vw + -12vw + 12v2 + -36w2) = 0

Combine like terms: 36vw + -12vw = 24vw
(24vw + 12v2 + -36w2) = 0

Solving
24vw + 12v2 + -36w2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '12'.
12(2vw + v2 + -3w2) = 0

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

Ignore the factor 12.
Subproblem 1
Set the factor '(v + -1w)' equal to zero and attempt to solve:

Simplifying
v + -1w = 0

Solving
v + -1w = 0

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

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

Combine like terms: -1w + w = 0
v + 0 = 0 + w
v = 0 + w
Remove the zero:
v = w

Simplifying
v = w
Subproblem 2
Set the factor '(v + 3w)' equal to zero and attempt to solve:

Simplifying
v + 3w = 0

Solving
v + 3w = 0

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

Add '-3w' to each side of the equation.
v + 3w + -3w = 0 + -3w

Combine like terms: 3w + -3w = 0
v + 0 = 0 + -3w
v = 0 + -3w
Remove the zero:
v = -3w

Simplifying
v = -3w
Solution
v = {w, -3w}