To factor 4x^2-12x-7, we need to find two binomials that multiply together to give us the original expression. The first term in each binomial must be 2x since (2x)(2x) gives us 4x^2. The last term in each binomial must be a combination of 7 and 1 that multiplies together to give us -7. We can use trial and error to find that 7 and 1 work. However, we need to make sure that the middle term in the factored form is -12x. We can use the following combination of signs to achieve this:
(2x - 7)(2x + 1)
Using FOIL (First, Outer, Inner, Last), we can check that this is correct:
(2x - 7)(2x + 1) = 4x^2 - 14x + 2x - 7 = 4x^2 - 12x - 7
Therefore, 4x^2-12x-7 in factored form is (2x - 7)(2x + 1).