w^2-wd-56d^2=0

Solution for w^2-wd-56d^2=0 equation:

Simplifying
w2 + -1wd + -56d2 = 0

Reorder the terms:
-1dw + -56d2 + w2 = 0

Solving
-1dw + -56d2 + w2 = 0

Solving for variable 'd'.

Factor a trinomial.
(-7d + -1w)(8d + -1w) = 0

Subproblem 1
Set the factor '(-7d + -1w)' equal to zero and attempt to solve:

Simplifying
-7d + -1w = 0

Solving
-7d + -1w = 0

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

Add 'w' to each side of the equation.
-7d + -1w + w = 0 + w

Combine like terms: -1w + w = 0
-7d + 0 = 0 + w
-7d = 0 + w
Remove the zero:
-7d = w

Divide each side by '-7'.
d = -0.1428571429w

Simplifying
d = -0.1428571429w
Subproblem 2
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
Solution
d = {-0.1428571429w, 0.125w}