We can use the general factoring method of finding two numbers that multiply to give -6 and add to give -11. In this case, the two numbers are -2 and -3.
Starting with the first term, 30x²:
Multiply the coefficient (30) by the two numbers we found (-2 and -3) to give 60 and -90.
Write the expression as (6x - 2)(5x + 3) and distribute the first term, 30x², as follows:
30x² = (6x - 2)(5x) + (6x - 2)(3)
Next, the middle term, -11x:
Distribute -11x as follows:
-11x = (6x)(-3) + (-2)(5x)
Finally, the last term, -6:
Distribute -6 as follows:
-6 = (6x - 2)(-3) + (-2)(3)
Putting all of this together, we have:
30x² - 11x - 6 = (6x - 2)(5x) + (6x - 2)(3) - (6x)(-3) - (-2)(5x) - (6x - 2)(-3) - (-2)(3)
Combining like terms:
30x² - 11x - 6 = (6x - 2)(5x + 3)
So, 30x² - 11x - 6 can be factored as (6x - 2)(5x + 3).