-16t^2-64t+512=0

Solution for -16t^2-64t+512=0 equation:

Simplifying
-16t2 + -64t + 512 = 0

Reorder the terms:
512 + -64t + -16t2 = 0

Solving
512 + -64t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '16'.
16(32 + -4t + -1t2) = 0

Factor a trinomial.
16((4 + -1t)(8 + t)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1t = 0 + -4
-1t = 0 + -4

Combine like terms: 0 + -4 = -4
-1t = -4

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Subproblem 2
Set the factor '(8 + t)' equal to zero and attempt to solve:

Simplifying
8 + t = 0

Solving
8 + t = 0

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

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

Combine like terms: 8 + -8 = 0
0 + t = 0 + -8
t = 0 + -8

Combine like terms: 0 + -8 = -8
t = -8

Simplifying
t = -8
Solution
t = {4, -8}