Question

How do you find all solutions of the equation `sin^2x+sinx=0`?

Answer 1

`S={x|x=kpivvx=-3/2pi+2kpi ^^kinZZ}`

Explanation:

`sin^2x+sinx=0`
can be rewritten:
`sinx(sinx+1)=0`
So we can state that `sinx=0` or `sinx=-1` because multiplying two numbers can result zero if and only if one of the two is zero.
So let's solve the two parts of the equation:
1. `sin(x)=0`
It is basically `x=kpi` where `kinZZ`
2. `sin(x)=-1`
It is basically `x=-3/2pi+2kpi` where `kinZZ`

So the solutions are:
`S={x|x=kpivvx=-3/2pi+2kpi ^^kinZZ}`