12v^2-36vw-48w^2=

Solution for 12v^2-36vw-48w^2= equation:

Simplifying
12v2 + -36vw + -48w2 = 0

Reorder the terms:
-36vw + 12v2 + -48w2 = 0

Solving
-36vw + 12v2 + -48w2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-3vw + v2 + -4w2) = 0

Factor a trinomial.
12((v + -4w)(v + w)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(v + -4w)' equal to zero and attempt to solve:

Simplifying
v + -4w = 0

Solving
v + -4w = 0

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

Add '4w' to each side of the equation.
v + -4w + 4w = 0 + 4w

Combine like terms: -4w + 4w = 0
v + 0 = 0 + 4w
v = 0 + 4w
Remove the zero:
v = 4w

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

Simplifying
v + w = 0

Solving
v + w = 0

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

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

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

Simplifying
v = -1w
Solution
v = {4w, -1w}