What is equal to:

((6a^2-30a) / a-2))((a^2+2a-8) / (2a^3-10a^2))

To simplify the given expression:

((6a^2-30a) / (a-2))((a^2+2a-8) / (2a^3-10a^2)),

we can start by simplifying each numerator and denominator separately.

Let's begin with the first fraction:

The numerator is 6a^2 - 30a, and we can factor out a common factor of 6a:
6a(a - 5).

The denominator is a - 2, which cannot be further simplified.

So, the first fraction becomes:
(6a(a - 5) / (a - 2)).

Moving on to the second fraction:

The numerator is a^2 + 2a - 8, and we can factor this trinomial by splitting the middle term:
(a^2 + 4a - 2a - 8) = a(a + 4) - 2(a + 4).

Now we can factor out the common factor of (a + 4):
(a + 4)(a - 2).

The denominator is 2a^3 - 10a^2, and we can factor out a common factor of 2a^2:
2a^2(a - 5).

So, the second fraction becomes:
((a + 4)(a - 2) / (2a^2)(a - 5)).

Now, we have simplified both fractions. To simplify the entire expression, we can multiply the fractions together:

((6a(a - 5) / (a - 2)) * ((a + 4)(a - 2) / (2a^2)(a - 5)).

Next, we cancel out the common factors in the numerator and denominator:

The (a - 5) term cancels out in the first fraction's numerator and second fraction's denominator.

The (a - 2) term cancels out in the first fraction's denominator and second fraction's numerator.

So, we are left with:

6a(a + 4) / (2a^2)(a - 5).

This can be further simplified by factoring out a common factor of 2a:
2a(3(a + 4) / a(a - 5)).

Finally, the expression simplifies to:

2(3)(a + 4) / (a)(a - 5) = 6(a + 4) / (a)(a - 5).

Therefore, the given expression is equal to 6(a + 4) / (a)(a - 5).