Maths problems [mixed]

if the coefficient of x^2 in the expansion of (-1+kx-x^2)(-2x+3) is -7, find k. The ans. of k is -2, how to calculate it?

the coefficient of x^2 is obtained by multiplying the (kx) in first expression with (-2x) in second expression plus (-x^2) in first expression with (+3) in second expression.
So (kx)(-2x) + (-x^2)(+3) = -7x^2
-2kx^2 - 3x^2 = -7x^2
-2k - 3 = -7
-2k = -4
k = 2 (so either your question or your answer is wrong)

if x:y:z= 2:3:5 and 3x+5y-2z=88, then y(z-x)=?. The ans is 576, how to calculate it?

x:y:z= 2:3:5 so y=3x/2; z=5x/2
3x+5y-2z=88
3x+5(3x/2)-2(5x/2)=88
(3+7.5-5)x=88
5.5x=88
x=16

x=16 => y = 3*16/2 = 24
z = 5*16/2 = 40

y(z-x) = 24 * (40 - 16) = 24 * 24 = 576