how do i solve?

(x+7)(x-2)>0

so -7<x<2

x^2 + 5x - 14 > 0
(x + 7)(x - 2) > 0

-7 < x < 2

(x + 7)(x - 2) = x^2 + 5x - 14
x = -7, x = 2
Take the larger of these two (2, in this case) and that is the factor that matches up with the sign.
(x - 2 ) > 0
x > 2
Same with the other factor, but flip the sign, since it was the lesser of the two.
(x + 7) < 0
x < -7
So, we get:
x < -7 or x > 2
Now, test the answer using points in and not in that range. (i.e. in range:-8 and 3, not in range: 0)
In our range, we need these to be true for our answer to be true.
64 - 40 - 14 > 0
10 > 0 True
9 + 15 - 14 > 0
10 > 0 True
Not in our range, we need these to be false for our answer to be true.
0 + 0 - 14 > 0
0 > 0 False
So, "x < -7 or x > 2" is the answer.
If you have a graphing calculator, or can draw the graph yourself, that is another good way to check if the answer is correct.

x^2 + 5x - 14 > 0
x^2+7x-2x-14 >0
x(x+7)-2(x+7) >0
(x+7)(x-2) > 0
x-2 > 0 means x > 2
x+7 > 0 means x > -7
The solution is x > 2

(x+7)(x-2) > 0
-7 > x > 2

x^2 + 5x - 14 > 0
(x + 7)(x - 2) > 0

x + 7 > 0
x > -7

x - 2 > 0
x > 2

∴ x > -7 , 2