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

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

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

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

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

Multiply (-2 + t) * (1 + t)
0 = -16(-2(1 + t) + t(1 + t))
0 = -16((1 * -2 + t * -2) + t(1 + t))
0 = -16((-2 + -2t) + t(1 + t))
0 = -16(-2 + -2t + (1 * t + t * t))
0 = -16(-2 + -2t + (1t + t2))

Combine like terms: -2t + 1t = -1t
0 = -16(-2 + -1t + t2)
0 = (-2 * -16 + -1t * -16 + t2 * -16)
0 = (32 + 16t + -16t2)

Solving
0 = 32 + 16t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -32 = -32
-32 + -16t + 16t2 = 32 + 16t + -16t2 + -32 + -16t + 16t2

Reorder the terms:
-32 + -16t + 16t2 = 32 + -32 + 16t + -16t + -16t2 + 16t2

Combine like terms: 32 + -32 = 0
-32 + -16t + 16t2 = 0 + 16t + -16t + -16t2 + 16t2
-32 + -16t + 16t2 = 16t + -16t + -16t2 + 16t2

Combine like terms: 16t + -16t = 0
-32 + -16t + 16t2 = 0 + -16t2 + 16t2
-32 + -16t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-32 + -16t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-2 + -1t + t2) = 0

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

Ignore the factor 16.
Subproblem 1
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
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 = {-1, 2}