v^2+6vd-16d^2=0

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Solution for v^2+6vd-16d^2=0 equation: 


Simplifying
v2 + 6vd + -16d2 = 0

Reorder the terms:
6dv + -16d2 + v2 = 0

Solving
6dv + -16d2 + v2 = 0

Solving for variable 'd'.

Factor a trinomial.
(-8d + -1v)(2d + -1v) = 0


Subproblem 1
Set the factor '(-8d + -1v)' equal to zero and attempt to solve:

Simplifying
-8d + -1v = 0

Solving
-8d + -1v = 0

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

Add 'v' to each side of the equation.
-8d + -1v + v = 0 + v

Combine like terms: -1v + v = 0
-8d + 0 = 0 + v
-8d = 0 + v
Remove the zero:
-8d = v

Divide each side by '-8'.
d = -0.125v

Simplifying
d = -0.125v

Subproblem 2
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
Solution
d = {-0.125v, 0.5v}

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