Let's solve the equation step by step:

The given equation is:
\[
13z + 19z + 52 = 180
\]

### Step 1: Combine like terms
\[
13z + 19z = 32z
\]
So, the equation becomes:
\[
32z + 52 = 180
\]

### Step 2: Subtract 52 from both sides
\[
32z = 180 - 52
\]
\[
32z = 128
\]

### Step 3: Divide both sides by 32
\[
z = \frac{128}{32}
\]
\[
z = 4
\]

Thus, the solution is:
\[
z = 4
\]

Would you like more details on this? 

Here are 5 related questions you can try:
1. Solve \( 7x + 12x + 8 = 47 \).
2. What is the value of \( y \) in \( 14y + 18 + 2y = 100 \)?
3. Solve \( 25z + 50z + 100 = 300 \).
4. How do you solve \( 5w + 3w + 40 = 120 \)?
5. Can you solve \( 8k + 12k + 24 = 180 \)?

**Tip:** Always start by simplifying the equation by combining like terms before proceeding with other operations!

Learn how to solve the linear equation 13z + 19z + 52 = 180 with a detailed step-by-step guide. This problem involves combining like terms and solving for the variable. Suitable for students in Grades 6-8.

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