can someone help me with w^2 + 3w - 10 = 0?

(w------)(w-----)
(w----5)(w----2)
The 5 and 2 have to be such that product = - 10 and sum = + 3
(w + 5)(w - 2) = 0
w = - 5 , w = 2

(w - 2 )( w + 5 )

w = ( 2, -5)

(w-2)(w+5)=0
w=2, w=5

w^2 + 3w - 10 = 0
w^2 + 5w - 2w - 10 = 0
(w^2 + 5w) - (2w + 10) = 0
w(w + 5) - 2(w + 5) = 0
(w + 5)(w - 2) = 0

w + 5 = 0
w = -5

w - 2 = 0
w = 2

∴ w = -5 , 2

The sum of 2 number(coefficient of W) is +ve.
U know the solutions- -5 ,2 or 5,-2
-5+2=-3 which is not possible.
So,u have last option left which is 5 and -2

(w+5) (w-2)

w^2 + 3w - 10 = 0 [ factor the equation ]
(w - 2)(w + 5) = 0
[ equate the content of each bracket to 0 ]
w - 2 = 0 --------or------- w + 5 = 0
w = 2 -------------or------- w = -5