Factorise 6a2−a−176 completely.

Sure, here is the step-by-step solution to factorize the given expression:

1. The given expression is 6a^2 - a - 176.

2. We need to factorize this quadratic equation in the form of (px + q)(rx + s).

3. For this, we need to find two numbers such that their product is equal to the product of the coefficient of a^2 (which is 6) and the constant term (which is -176), and their sum is equal to the coefficient of a (which is -1).

4. The two numbers that satisfy these conditions are -8 and 22, because -822 = -1766 and -8 + 22 = -1.

5. So, we can write the middle term (-a) as -8a + 22a.

6. The expression becomes 6a^2 - 8a + 22a - 176.

7. Now, we can factor by grouping. The first two terms can be grouped together, and the last two terms can be grouped together.

8. This gives us 2a(3a - 4) + 22(3a - 4).

9. Now, you can see that (3a - 4) is a common factor.

10. So, the factorized form of the given expression is (2a + 22)(3a - 4).

So, 6a^2 - a - 176 = (2a + 22)(3a - 4).