0=-2(t-1)-16t(t-1)

Solution for 0=-2(t-1)-16t(t-1) equation:

Simplifying
0 = -2(t + -1) + -16t(t + -1)

Reorder the terms:
0 = -2(-1 + t) + -16t(t + -1)
0 = (-1 * -2 + t * -2) + -16t(t + -1)
0 = (2 + -2t) + -16t(t + -1)

Reorder the terms:
0 = 2 + -2t + -16t(-1 + t)
0 = 2 + -2t + (-1 * -16t + t * -16t)
0 = 2 + -2t + (16t + -16t2)

Combine like terms: -2t + 16t = 14t
0 = 2 + 14t + -16t2

Solving
0 = 2 + 14t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -2 = -2
-2 + -14t + 16t2 = 2 + 14t + -16t2 + -2 + -14t + 16t2

Reorder the terms:
-2 + -14t + 16t2 = 2 + -2 + 14t + -14t + -16t2 + 16t2

Combine like terms: 2 + -2 = 0
-2 + -14t + 16t2 = 0 + 14t + -14t + -16t2 + 16t2
-2 + -14t + 16t2 = 14t + -14t + -16t2 + 16t2

Combine like terms: 14t + -14t = 0
-2 + -14t + 16t2 = 0 + -16t2 + 16t2
-2 + -14t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-2 + -14t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -7t + 8t2) = 0

Factor a trinomial.
2((-1 + -8t)(1 + -1t)) = 0

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

Simplifying
-1 + -8t = 0

Solving
-1 + -8t = 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 + -8t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8t = 0 + 1
-8t = 0 + 1

Combine like terms: 0 + 1 = 1
-8t = 1

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

Simplifying
t = -0.125
Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve:

Simplifying
1 + -1t = 0

Solving
1 + -1t = 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 + -1t = 0 + -1

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

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

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

Simplifying
t = 1
Solution
t = {-0.125, 1}