Find all roots of the following equation?

Questions
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1

I’m currently doing some Mathematica exercises, and I’m stuck on this one task where you’re supposed to plot the functions h(t)= |3-t^2|+|t-1|-t^2 , g(t)=3sin(t) in the same grap, and then find all the roots. This is what I’ve got so far:

UHvxo.png
UHvxo.png930×373 13.9 KB

The instructions say that I should use FindRoot to exactly decide all the roots, but I don’t think I’ve done it right. What should I change with the function in order to make it find all of the roots?

Thanks in advance.

2

Good starting points solves the problem:

FindRoot[Abs[3 - t^2] + Abs[t - 1] - t^2 == 3*Sin[t], {t, #}] & /@ {-5, -4, 1, 3}

(*  {{t -> -4.92954}, {t -> -3.77452}, {t -> 0.762901}, {t -> 3.35745}} *)