Let's solve the equation:

$3(2x + 9) + 12(4x - 8) = 55$

Step 1: Distribute the constants.

First, distribute the $3$ and $12$ to terms inside the parentheses:

$3(2x + 9) = 6x + 27$ $12(4x - 8) = 48x - 96$

So the equation becomes:

$6x + 27 + 48x - 96 = 55$

Step 2: Combine like terms.

Combine the $x$-terms and the constant terms:

$6x + 48x = 54x$ $27 - 96 = -69$

Now the equation is:

$54x - 69 = 55$

Step 3: Isolate the $x$-term.

Add 69 to both sides of the equation to move the constant to the right side:

$54x = 55 + 69$ $54x = 124$

Step 4: Solve for $x$.

Divide both sides by 54:

$x = \frac{124}{54}$

Simplify the fraction:

$x = \frac{62}{27}$

So, the solution is:

$x = \frac{62}{27}$

Would you like further details on any steps? Here are some related questions:

1. How can you verify the solution by substituting $x$ back into the original equation?
2. What is the importance of distributing constants in equations?
3. How do you simplify complex fractions like $\frac{62}{27}$?
4. What is the difference between combining like terms and isolating variables?
5. Can you express the solution $x = \frac{62}{27}$ as a decimal?

Tip: When solving equations, always distribute and combine like terms first for simplification.