w^2+6wd-16d^2=0

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Solution for w^2+6wd-16d^2=0 equation: 


Simplifying
w2 + 6wd + -16d2 = 0

Reorder the terms:
6dw + -16d2 + w2 = 0

Solving
6dw + -16d2 + w2 = 0

Solving for variable 'd'.

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


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

Simplifying
-8d + -1w = 0

Solving
-8d + -1w = 0

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

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

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

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

Simplifying
d = -0.125w

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

Simplifying
2d + -1w = 0

Solving
2d + -1w = 0

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

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

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

Divide each side by '2'.
d = 0.5w

Simplifying
d = 0.5w
Solution
d = {-0.125w, 0.5w}

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