v^2-7vz+12z^2=

Solution for v^2-7vz+12z^2= equation:

Simplifying
v2 + -7vz + 12z2 = 0

Reorder the terms:
-7vz + v2 + 12z2 = 0

Solving
-7vz + 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}