Can someone please explain how to do this?

  see below

Step-by-step explanation:

Factor the equation and use the zero product rule.

  0 = 2sin(t)² +sin(t) . . . . . . . the velocity is zero

  0 = sin(t)·(2sin(t) +1) . . . . . factor the equation

The product will be zero when either factor is zero:

sin(t) = 0

  This is true for t = 0, π, 2π.

__

2sin(t) +1 = 0

  This is true for sin(t) = -1/2, at t = 7π/6 and 11π/6.

Then the solution is ...

  t ∈ {0, π, 7π/6, 11π/6, 2π}

what "following statement"?

step-by-step explanation: