t^2+6td-27d^2=

Solution for t^2+6td-27d^2= equation:

Simplifying
t2 + 6td + -27d2 = 0

Reorder the terms:
6dt + -27d2 + t2 = 0

Solving
6dt + -27d2 + t2 = 0

Solving for variable 'd'.

Factor a trinomial.
(-9d + -1t)(3d + -1t) = 0

Subproblem 1
Set the factor '(-9d + -1t)' equal to zero and attempt to solve:

Simplifying
-9d + -1t = 0

Solving
-9d + -1t = 0

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

Add 't' to each side of the equation.
-9d + -1t + t = 0 + t

Combine like terms: -1t + t = 0
-9d + 0 = 0 + t
-9d = 0 + t
Remove the zero:
-9d = t

Divide each side by '-9'.
d = -0.1111111111t

Simplifying
d = -0.1111111111t
Subproblem 2
Set the factor '(3d + -1t)' equal to zero and attempt to solve:

Simplifying
3d + -1t = 0

Solving
3d + -1t = 0

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

Add 't' to each side of the equation.
3d + -1t + t = 0 + t

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

Divide each side by '3'.
d = 0.3333333333t

Simplifying
d = 0.3333333333t
Solution
d = {-0.1111111111t, 0.3333333333t}