Let's solve the equation step by step.
You have the equation:
\[ \frac{9b + 12}{3} = -3b + 13 \]
First, let's multiply both sides by 3 to eliminate the fraction:
\[ 9b + 12 = 3(-3b + 13) \]
Now, distribute on the right side:
\[ 9b + 12 = -9b + 39 \]
Next, let's add \(9b\) to both sides to get all terms involving \(b\) on one side:
\[ 9b + 9b + 12 = 39 \]
This simplifies to:
\[ 18b + 12 = 39 \]
Now, subtract 12 from both sides:
\[ 18b = 39 - 12 \]
\[ 18b = 27 \]
Now, divide both sides by 18:
\[ b = \frac{27}{18} \]
This can be simplified:
\[ b = \frac{3}{2} \quad \text{or} \quad b = 1.5 \]
Thus, the final answer is:
\[ b = \frac{3}{2} \quad \text{or} \quad b = 1.5 \]