Here is the problem worked out and the explanation follows.

W^{2} -2W = 15

W^{2} -2W -15 =0

(W-5) (W+3) = 0

W-5 = 0 or w+3 = 0

W = 5 or w= -3

To check plug each number into the original equation for each W

(5)^{2} - 2(5) = 15 or (-3)^{2} -2(-3) =15

25 -10 =15 9 +6 =15

15 = 15 YES 15= 15 YES

To solve by factoring you must first have all of the terms on one side so that the equation is equal to zero.

W^{2} -2W = 15

W^{2} -2W -15 = 15 -15 (subtract 15 from both sides)

W^{2} -2W -15 = 0

The exponent of two on the first term tells us that we will have 2 factors ( ) ( )

The last term (-15) being negative tells us our signs will be one positive and one negative ( + ) ( - )

Because our signs are one positive and one negative, when we find the factors of the last term (15) we know we will subtract one from the other.

We need to find the factors of -15 so that when we subtract one from the other we get the middle term which is -2. The factors are -5 and 3.

(w -5) (w+3) = 0

Since the factors multiplied together equal zero, it means either the first factor or the second equal zero so we set each factor = to zero

w-5 = 0 or w+3 = 0 (solve for w)

w= 5 or w= -3

To check see explanation above