What value of x makes the equation f(g(x)) equal to 0, given the functions f(x) = 16x + 30 and g(x) = 14x + 6?

To solve the equation f(g(x)) = 0, we first need to understand the relationship between the two functions given:

First, we will find the expression for g(x):

g(x) = 14x + 6

Next, we substitute g(x) into f(x):

f(g(x)) = f(14x + 6) = 16(14x + 6) + 30

Now, we need to simplify the expression:

f(g(x)) = 16(14x + 6) + 30

= 16 * 14x + 16 * 6 + 30

= 224x + 96 + 30

= 224x + 126

The next step is to set this expression equal to 0:

224x + 126 = 0

Now, we solve for x:

224x = -126

x = -126 / 224

x = -rac{63}{112}

To simplify it further:

x = -rac{9}{16}

Thus, the value of x that makes f(g(x)) = 0 is:

x = -rac{9}{16}