-16t(t+1)(t-5)=0

Solution for -16t(t+1)(t-5)=0 equation:

Simplifying
-16t(t + 1)(t + -5) = 0

Reorder the terms:
-16t(1 + t)(t + -5) = 0

Reorder the terms:
-16t(1 + t)(-5 + t) = 0

Multiply (1 + t) * (-5 + t)
-16t(1(-5 + t) + t(-5 + t)) = 0
-16t((-5 * 1 + t * 1) + t(-5 + t)) = 0
-16t((-5 + 1t) + t(-5 + t)) = 0
-16t(-5 + 1t + (-5 * t + t * t)) = 0
-16t(-5 + 1t + (-5t + t2)) = 0

Combine like terms: 1t + -5t = -4t
-16t(-5 + -4t + t2) = 0
(-5 * -16t + -4t * -16t + t2 * -16t) = 0
(80t + 64t2 + -16t3) = 0

Solving
80t + 64t2 + -16t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '16t'.
16t(5 + 4t + -1t2) = 0

Factor a trinomial.
16t((5 + -1t)(1 + t)) = 0

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

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
Set the factor '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 0

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

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

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Subproblem 3
Set the factor '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 0

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

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

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

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

Simplifying
t = -1
Solution
t = {0, 5, -1}