The problem asks us to simplify the expression $3(4x-5)+2$.

1. Problem Description

The problem asks us to simplify the expression $3(4x-5)+2$.

2. Solution Steps

We will first use the distributive property to multiply $3$ by the terms inside the parentheses:

$3(4x-5) = 3(4x) - 3(5) = 12x - 15$.

Now we substitute this back into the original expression:

$3(4x-5)+2 = (12x - 15) + 2$.

Combine the constant terms:

$-15 + 2 = -13$.

Therefore, $12x - 15 + 2 = 12x - 13$.

3. Final Answer

The simplified expression is $12x - 13$.