Please help: factorisation

I am having trouble with learning how to factorise equations.
How would you factorise 3t^2 - 5t - 2 ?
Please show steps so I can learn how to do it as well.
Thank you in advance

Set the expression as equal to zero:

3t^2 - 5t - 2 = 0

Use the reverse FOIL method. Since three is a prime number, its only factors are
three and one. So the t terms are as shown below:

(3t )(t ) = 0

The last term, two, is also a prime number; its only factors are two and one. The product
of the factors of two must equal -2 and the sum, combined with the t coefficients must
equal -5. Since the signs of the second and third terms are both negative, we know that
the factors will have unlike signs. Inserting the factors of -2, we get:

(3t + 1)(t - 2) = 0

Setting, in turn, each factor equal to zero, we get:

3t + 1 = 0
3t = -1
t = -1/3

and

t - 2 = 0
t = 2

To check, insert each value, in turn, into the original equation. If you get an identity, then
the value is correct.

t = -1/3
3(-1/3)^2 - 5(-1/3) - 2 = 0
3(1/9) + 5/3 - 2 = 0
3/9 + 5/3 - 2 = 0
1/3 + 5/3 - 2 = 0
6/3 - 2 = 0
2 - 2 = 0
0 = 0

t = 2
3(2)^2 - 5(2) - 2 = 0
3(4) - 10 - 2 = 0
12 - 10 - 2 = 0
2 - 2 = 0
0 = 0

Therefore, both values of t are correct.