v^2-vz-12z^2=0

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Solution for v^2-vz-12z^2=0 equation: 


Simplifying
v2 + -1vz + -12z2 = 0

Reorder the terms:
-1vz + v2 + -12z2 = 0

Solving
-1vz + v2 + -12z2 = 0

Solving for variable 'v'.

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


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

Simplifying
v + -4z = 0

Solving
v + -4z = 0

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

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

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

Simplifying
v = 4z

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

Simplifying
v + 3z = 0

Solving
v + 3z = 0

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

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

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

Simplifying
v = -3z
Solution
v = {4z, -3z}

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