Factorization 4x ^ 2 + xy-y ^ 2 + 7x + 8y-15

Factorization 4x ^ 2 + xy-y ^ 2 + 7x + 8y-15

This is the solution to solve the following: the original formula: the original formula = 4x \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\+ BD, a-c = 1, ② AC = 4, ③ BC + ad = 7, ④ B-D = 8, ⑤ BD = - 15, the integer solution of a and C can be obtained by ① and ②, so that the factorization can be carried out, but the integer solution of a and C can not be obtained by ① and ② of this problem, the condition of your problem must be wrong, which number is wrong? Please check. But my two methods are very good! I hope you can master them

Factorization: (1) x ^ 2-2xy-35y ^ 2 (2) 2x ^ 2-7x-15 (3) 20x ^ 2-43xy + 14y ^ 2 (4) 18x ^ 2-19x + 15
（1） X ^ 2-2xy-35y ^ 2
（2） 2X ^ 2-7x-15
（3） 20x ^ 2-43xy + 14y ^ 2
（4） 18x ^ 2-19x + 5
（5） 6X ^ 2-13x + 6
（6） 5x ^ 2 + 4xy-28y ^ 2
（7） - 35m ^ 2n ^ 2 + 11mn + 6
（8） 6 + 11a-35a ^ 2
（9） 6-11a-35a ^ 2
（10） - 1 + y + 20Y ^ 2
Please factorize the above ten questions,

（1） X ^ 2-2xy-35y ^ 2 = (x-7y) (x + 5Y) (2) 2x ^ 2-7x-15 = (x2 + 3) (X-5) (3) 20x ^ 2-43xy + 14y ^ 2 = (4x-7y) (5x-2y) (4) 18x ^ 2-19x + 5 = ((2x-1) (9x-5) (5) 6x ^ 2-13x + 6 = (3x-2) (2x-3) (6) 5x ^ 2 + 4xy-28y ^ 2 = (5x-14y) (x-2y) (7) - 35m ^ 2n ^ 2 + 11mn + 6

Factorization 6x ^ 2-7x + 2

6x^2-7x+2 =(2X-1)(3X-2)

Given that at least one of the equations ax ^ 2 - (3a ^ 2-8a) x + 2A ^ 2-13a + 15 = 0 (where a is a non negative integer) is an integer root, then a=_______ .
3,5, but I don't know how to solve it,

The first coefficient should be a ^ 2
a^2x^2-(3a^2-8a)x+(2a-3)(a-5)=0
[ax-(2a-3)][ax-(a-5)]=0
x=2-3/a,x=1-5/a
To make the equation have integer roots, 3 / A and 5 / a are integers