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

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

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

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

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

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

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

Solving
32 + 16t + -16t2 = 0

Solving for variable 't'.

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

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

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