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

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

Simplify the fractions:

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

(x/2 + 4) + (3/5 - 2x/5) = 3

Now find a common denominator for the fractions in the equation:

(x/2 + 4) + (3 - 2x)/5 = 3

Now, multiply the first fraction by 5/5 and the second fraction by 2/2 to get a common denominator:

(5x/10 + 20/10) + (6 - 4x)/10 = 3

Combine the fractions:

(5x + 20 + 6 - 4x) / 10 = 3

Simplify:

(x + 26) / 10 = 3

Now, multiply both sides by 10:

x + 26 = 30

Subtract 26 from both sides:

x = 4

Therefore, the solution to the equation is x = 4.