t^2-5td-24d^2=

Solution for t^2-5td-24d^2= equation:

Simplifying
t2 + -5td + -24d2 = 0

Reorder the terms:
-5dt + -24d2 + t2 = 0

Solving
-5dt + -24d2 + t2 = 0

Solving for variable 'd'.

Factor a trinomial.
(-3d + -1t)(8d + -1t) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(8d + -1t)' equal to zero and attempt to solve:

Simplifying
8d + -1t = 0

Solving
8d + -1t = 0

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

Add 't' to each side of the equation.
8d + -1t + t = 0 + t

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

Divide each side by '8'.
d = 0.125t

Simplifying
d = 0.125t
Solution
d = {-0.3333333333t, 0.125t}