I would like to solve x^2 +3x -4=0 using greatest common factor

While there is no factor that is common to all the terms of this polynomial, it can be factored. When finding binomial factors of this kind of polynomial, we start by finding what pairs of numbers can multiply to yield the number at the end, which in this case is -4. The possibilities are:

-4 x 1 = -4

4 x -1= -4

2 x -2= -4

The other requirement for the numbers we choose is that they must add up to +3. Using the three possibilities we listed, we can add:

-4 + 1 = -3

4 + -1= +3

2 + -2= 0

4 and -1 fulfill the second requirement. We build the factors like this:

(x )(x )

...then inside the template, use the two numbers, with signs, that we came up with:

(x + 4)(x - 1) = 0

If these two factors multiplied together equal 0, then one of them must be 0. We set each to 0 in turn, and solve:

x + 4 = 0; x = -4

x - 1 = 0; x = 1