The first step to factorize the given expression, 10t3 - 8t2 15t - 12, is to find common factors in different parts of the expression. To do this, we will first break down the expression into two parts: 10t3 - 8t2 and 15t - 12.
Looking at the first part, 10t3 - 8t2, we can see that it can be rewritten by factoring out the common term of 2t2. This gives us 2t2(5t - 4).
When we turn our attention to the second part, 15t - 12, we can see that it can also be rewritten by factoring out the common term of 3. This gives us 3(5t - 4).
Now, we can see that (5t - 4) is a common factor in both parts of the original expression. This means that we can factor out (5t - 4) as a common factor of the expression. This gives us (2t2 + 3)(5t - 4).
Therefore, the complete factorization of the expression 10t3 - 8t2 15t - 12 is (2t2 + 3)(5t - 4).