t^2-3td-10d^2=0

Solution for t^2-3td-10d^2=0 equation:

Simplifying
t2 + -3td + -10d2 = 0

Reorder the terms:
-3dt + -10d2 + t2 = 0

Solving
-3dt + -10d2 + t2 = 0

Solving for variable 'd'.

Factor a trinomial.
(-2d + -1t)(5d + -1t) = 0

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

Simplifying
-2d + -1t = 0

Solving
-2d + -1t = 0

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

Add 't' to each side of the equation.
-2d + -1t + t = 0 + t

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

Divide each side by '-2'.
d = -0.5t

Simplifying
d = -0.5t
Subproblem 2
Set the factor '(5d + -1t)' equal to zero and attempt to solve:

Simplifying
5d + -1t = 0

Solving
5d + -1t = 0

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

Add 't' to each side of the equation.
5d + -1t + t = 0 + t

Combine like terms: -1t + t = 0
5d + 0 = 0 + t
5d = 0 + t
Remove the zero:
5d = t

Divide each side by '5'.
d = 0.2t

Simplifying
d = 0.2t
Solution
d = {-0.5t, 0.2t}