To solve this equation, we first need to simplify the expression on the left side of the equation:

4 3/8 ÷ 5 1/4

Convert the mixed numbers to improper fractions:

4 3/8 = (4*8 + 3)/8 = 35/8

5 1/4 = (5*4 + 1)/4 = 21/4

Now divide the fractions:

(35/8) ÷ (21/4) = (35/8) * (4/21) = 35/42 = 5/6

So, 4 3/8 ÷ 5 1/4 = 5/6

Now rewrite the original equation with the simplified value:

x / 12 * (3(2/5)x + 3) - (3/5)x = 8

Now, simplify the equation further:

x / 12 (3 + 3x/5) - (3/5)x = 8
x/12 (15 + 3x) - (3/5)x = 8
(x * (15 + 3x))/12 - (3x)/5 = 8
(15x + 3x^2)/12 - (3x)/5 = 8
(15x + 3x^2)/12 - (36x)/60 = 8
(15x + 3x^2)/12 - (36x)/60 = 8
(15x + 3x^2)/12 - (6x)/30 = 8
(30x + 3x^2 - 72x) / 60 = 8
(3x^2 - 42x) / 60 = 8
3x^2 - 42x = 480
3x^2 - 42x - 480 = 0

Now we have a quadratic equation, which can be solved by factoring, completing the square, or using the quadratic formula.