-16t^2+288t-512=0

Solution for -16t^2+288t-512=0 equation:

Simplifying
-16t2 + 288t + -512 = 0

Reorder the terms:
-512 + 288t + -16t2 = 0

Solving
-512 + 288t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '16'.
16(-32 + 18t + -1t2) = 0

Factor a trinomial.
16((-16 + t)(2 + -1t)) = 0

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

Simplifying
-16 + t = 0

Solving
-16 + t = 0

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

Add '16' to each side of the equation.
-16 + 16 + t = 0 + 16

Combine like terms: -16 + 16 = 0
0 + t = 0 + 16
t = 0 + 16

Combine like terms: 0 + 16 = 16
t = 16

Simplifying
t = 16
Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

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

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {16, 2}