Hi Michael,
Factor
12x2+14xy-6y2
First factor out GCF=2
2[6x2+7xy-3y2]
To factor the trinomial we are going to use the Double Slide Method.
Multiply the coefficient of the 1st term times the last term
6x2+7xy-3y2
x2+7xy-18y2
Since the last term is negative, one factor has to be negative and one positive
since the middle term is positive, the largest factor has to be positive.
Now we need factors of -18 that sum 7
-1 18 no
-2 9 YES -2+9=7
(x-2y)(x+9y)
since we multiplied by 6 before, now we have to divide by six and reduce.
(x-2y/6)(x+9y/6)
(x-y/3)(x+3y/2) the fractions are reduced fully, now Slide the denominators over in front of the x's
(3x-y)(2x+3y)
Got to remember to put the GCF in the final answer: 2(3x-y)(2x+3y)
That's the double slide method.
ANSWER: 2(3x-y)(2x+3y)