Let $g(2x + 5) = 4x^2 - 3x + 2$. Find $g(-3)$.
I notice that the function $g$ has an argument of $2x + 5$, which means that whatever input I give to $g$, it will first multiply it by $2$ and then add $5$. So, if I want to find $g(-3)$, I need to figure out what value of $x$ makes $2x + 5 = -3$. I can do this by solving for $x$ in this equation. Subtracting $5$ from both sides gives me $2x = -8$. Dividing both sides by $2$ gives me $x = -4$. So, $g(-3) = g(2 \cdot -4 + 5)$. Now, I can plug in $x = -4$ into the expression for $g(2x + 5)$ and simplify. I get $g(2 \cdot -4 + 5) = 4 \cdot (-4)^2 - 3 \cdot (-4) + 2$. This simplifies to $g(-3) = 4 \cdot 16 + 12 + 2$. This simplifies further to $g(-3) = 64 + 14$. This gives me the final answer of $g(-3) = 78$. 