v^2-vd-6d^2=0

Solution for v^2-vd-6d^2=0 equation:

Simplifying
v2 + -1vd + -6d2 = 0

Reorder the terms:
-1dv + -6d2 + v2 = 0

Solving
-1dv + -6d2 + v2 = 0

Solving for variable 'd'.

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

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

Simplifying
-2d + -1v = 0

Solving
-2d + -1v = 0

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

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

Combine like terms: -1v + v = 0
-2d + 0 = 0 + v
-2d = 0 + v
Remove the zero:
-2d = v

Divide each side by '-2'.
d = -0.5v

Simplifying
d = -0.5v
Subproblem 2
Set the factor '(3d + -1v)' equal to zero and attempt to solve:

Simplifying
3d + -1v = 0

Solving
3d + -1v = 0

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

Add 'v' to each side of the equation.
3d + -1v + v = 0 + v

Combine like terms: -1v + v = 0
3d + 0 = 0 + v
3d = 0 + v
Remove the zero:
3d = v

Divide each side by '3'.
d = 0.3333333333v

Simplifying
d = 0.3333333333v
Solution
d = {-0.5v, 0.3333333333v}