For fx=6x-5 and gx=3x^2-4 find the following (fog)(x)

Having problems understanding
(gof(x)=g(f(x))= 3(f(x))^2-4
3(6x-5)^2-4
(36x-9-25)-4

f = 3(6x-5)^2 -4

= 3 (36 x^2 -60 x +25) - 4
= 108 x^2 -180 x +71

given two consecutive integers. The sum of three times the first integer and four times the second integer is 95. Find the integers

To find (fog)(x), which is equivalent to g(f(x)), you need to substitute the function f(x) into the function g(x).

First, let's rewrite f(x) as 6x - 5.
Now, substitute f(x) into the function g(x):
g(f(x)) = 3(f(x))^2 - 4
= 3(6x - 5)^2 - 4

To simplify further, you need to expand the squared term, (6x - 5)^2:
(6x - 5)^2 = (6x - 5)(6x - 5)
= 36x^2 - 30x - 30x + 25
= 36x^2 - 60x + 25

Now, substitute this expression into the g(f(x)) equation:
g(f(x)) = 3(36x^2 - 60x + 25) - 4
= 108x^2 - 180x + 75 - 4
= 108x^2 - 180x + 71

Therefore, (fog)(x) or g(f(x)) is equal to 108x^2 - 180x + 71.