Let's go through the equation step-by-step based on the process you've outlined.
Starting from the beginning with the equation:
\[ 5(5h - 15) = 9h + 9 \]
First, using the distributive property:
\[ 5 \cdot 5h - 5 \cdot 15 = 9h + 9 \]
This simplifies to:
\[ 25h - 75 = 9h + 9 \]
Now, subtract \(9h\) from both sides to get:
\[ 25h - 9h - 75 = 9 \]
This simplifies to:
\[ 16h - 75 = 9 \]
Next, add \(75\) to both sides:
\[ 16h = 9 + 75 \]
which simplifies to:
\[ 16h = 84 \]
Now, divide both sides by \(16\):
\[ h = \frac{84}{16} \]
Reducing this fraction:
\[ h = \frac{21}{4} \]
So, the value of \(h\) is:
\[ h = 5.25 \]
Thus, the final answer is that \(h = \frac{21}{4}\) or \(h = 5.25\).