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Factor out the 4 or -4 because every component in the problem is divisible by 4.
So: -4(X^2 + X - 6)
Now the X^2 + X - 6 can be broken down into two parts. The factors of 6 are -6 & 1, 6 & -1, 3 & -2, and. -3 & 2. Which combination will equal 1 with a negative 6. The answer is 3 and -2 because 3 + -2 = 1 and 3 * -2 = -6.

Now your equation looks like this:
-4(x + 3)(X -2) and thus your equation is fully factored.