To solve the expression $2a + 3b$ given $a = 3$ and $b = -2$:

Substitute the values of $a$ and $b$ into the expression:

$2(3) + 3(-2)$

Now, calculate each part:

$2(3) = 6$ $3(-2) = -6$

Add them together:

$6 + (-6) = 0$

So, the value of the expression is $0$.

Would you like more details or have any questions?

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Here are 5 related questions to explore further:

1. What happens if both $a$ and $b$ are negative?
2. How do you factor an expression like $2a + 3b$?
3. How can this expression change if $a$ and $b$ are functions instead of constants?
4. What is the result of $2a + 3b$ if $a = -3$ and $b = 2$?
5. How does the distributive property work for expressions like this?

Tip: Always double-check the signs of the numbers you substitute to avoid common mistakes.