I am having trouble with a question, It is find the illegal values of c in the multiplication statement

Question

c^2-3c-10    c^2-c-2
--------- * ---------- 
c^2+5c-14    c^2-2c-15

Answer 1

The multiplication statement is 

Now i factorise the each numarator and denominator.

Substitute the above values in the multiplication statement.
.

The illegal values is the values that make the two denominator's equal to zero.

Solve both denominators are (c+7)(c-2) and (c-5)(c+3).

First denominator is (c+7)(c-2) = 0

Aplly zero product property.

c+7 = 0 and c-2 = 0

c = -7 and c = 2.

Second denominator is (c-5)(c+3).

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

c-5 = 0 and c + 3 = 0.

c = 5 and c = -3

So the illegal values are 2 , -7 , 5 , -3.