Completely factor the following expression.

1.4x^2-8x-12+6x

First combine like terms.

4x^2-8x-12+6x = 4x^2 -2x -12 = (4x+6)(x-2)

To completely factor the expression 1.4x^2 - 8x - 12 + 6x, we start by combining like terms:

1.4x^2 - 8x - 12 + 6x

Simplifying further:

= 1.4x^2 - 2x - 12

Next, we need to find two numbers that multiply to give -16.8 (which is the product of 1.4 and -12) and add up to -2 (which is the coefficient of x).

Let's use a factorization method called "splitting the middle term." We can rewrite -2x as the sum of two terms:
-2x = (-4x) + (2x)

Now, the expression becomes:

= 1.4x^2 - 4x + 2x - 12

We can group the terms:

= (1.4x^2 - 4x) + (2x - 12)

Now, we can factor common terms from each group:

= x(1.4x - 4) + 2(1.4x - 4)

Notice that we have a common factor of (1.4x - 4) in both terms. We can factor it out:

= (x + 2)(1.4x - 4)

Therefore, the completely factored expression is (x + 2)(1.4x - 4).