How to find the value of a constant (a) in a binomial expansion?

Question

Q) In the expansion of (1-x/a) (5+x)⁶, the coefficient of x² is zero. Find the value of a.

So I thought it would be a matter of expanding the second parentheses because it is the binomial then multiply by the first (more simple) parentheses, however I seem to be getting x in terms of a. The answer is a=2 and any help would be very much appreciated :)

Answer 1

(5+x)^6 = 5^6 + 6(5^5)x + 15(5^4)x^2 + 20(5^3)x^3 + 15(5^2)x^4 + 6(5)x^5 + x^6

(1-x/a)(5+x)^6 will have an x^2 term that is the sum of 15(5^4)x^2 -(x/a)(6(5^5)x

= 15(625)x^2 - 6(3125)x^2/a

=9375x^2 - 18750x^2/a

= (9375 - 18750/a)x^2

then 9375-18750/a = 0

9375a = 18750

a = 18750/9375 = 2