r^2+6rd-16d^2=

Solution for r^2+6rd-16d^2= equation:

Simplifying
r2 + 6rd + -16d2 = 0

Reorder the terms:
6dr + -16d2 + r2 = 0

Solving
6dr + -16d2 + r2 = 0

Solving for variable 'd'.

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

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

Simplifying
-8d + -1r = 0

Solving
-8d + -1r = 0

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

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

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

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

Simplifying
d = -0.125r
Subproblem 2
Set the factor '(2d + -1r)' equal to zero and attempt to solve:

Simplifying
2d + -1r = 0

Solving
2d + -1r = 0

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

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

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

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

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