This factorises as:
(x - 1)(x + 1)(x - 2)(x + 7) = 0
I'm sure you can take it from there!
x^4+5x^3-15x^2-5x+14 = 0
Write -15x^2 as -14x^2 - x^2
x^4+5x^3-14x^2 - x^2 -5x+14 = 0
x^2(x^2+ 5x - 14) - 1(x^2 + 5x - 14) = 0
(x^2 - 1) ( x^2 + 5x - 14) = 0
(x + 1) (x - 1) (x + 7) ( x - 2) = 0
Set each factor to 0 and solve for x and we get that x = -1, 1, - 7 or 2