To solve this equation, first distribute the terms inside the parentheses:

2.7(0.1x + 3.2) + 0.6(13 - x) = 16.02

0.27x + 8.64 + 7.8 - 0.6x = 16.02

Combine like terms:

-0.33x + 16.44 = 16.02

Subtract 16.44 from both sides:

-0.33x = -0.42

Divide by -0.33:

x = 1.27

Therefore, the value of x that satisfies the equation is 1.27.