First step is to combine like terms.
x + 6x^2 - 4x - 24 = 6x^2 - 3x - 24
Now you want to find the greatest common factor that each coefficient (6, -3, and -24) shares. They all have a 3 in common. So we are gonna divide each term by 3.
6x^2 - 3x - 24 = 3(2x^2 - x - 8)
The next step is to see if we can factor that polynomial within the parentheses any further. Polynomials are set up in this form: ax^2 + bx + c, where A, B, and C are coefficients. We multiply the A coefficient (2) and the C coefficient (-8), then find what factors have a sum equal to the B coefficient (-1). There are no factors of -16 that add up to -1. So, you must stop there; your equation is factored completely.
Your answer is 3(2x^2 - x - 8)
