(x+5)(x+2)(x+a) = x^3 + bx^2 + cx - 30

First you expand the triple brackets to get;
x^3 + 5x^2 + 2x^2 + 10x + ax^2 + 5ax + 2ax + 10a = x^3 + bx^2 + cx - 30

You can now cancel down the equation to get;
7x^2 + 10x + ax^2 + 7ax + 10a = bx^2 + cx - 30

Next you find 10a.
So 10a = -30 so a = -3 because 10 x -3 = -30

Then, you split the equations;
7x^2 + ax^2 = bx^2 & 10x + 7ax = cx

Now, you can factor in -3 to the equations containing 'a' to get;
7x^2 - 3x^2 = bx^2 so **b = 4** because 7 - 3 = 4

and you also get;
10x + 7ax = cx so **c = -11** because 7 x -3 = -21. Then you do 10 + -21 to get -11.

So the answers to (x+5)(x+2)(x+a) = x^3 + bx^2 + cx - 30 are;
a = -3
b = 4
c = -11

Hope this helps :)