To solve the equation:

\[
-6(z - 3) - 2 = -4(6 + 5z) + 3
\]

we’ll go through each step systematically:

### Step 1: Distribute the terms
Expand both sides:

\[
-6z + 18 - 2 = -24 - 20z + 3
\]

### Step 2: Simplify each side
Combine like terms on each side:

\[
-6z + 16 = -20z - 21
\]

### Step 3: Move the variable terms to one side
Add \(20z\) to both sides:

\[
14z + 16 = -21
\]

### Step 4: Move the constant terms to the other side
Subtract \(16\) from both sides:

\[
14z = -37
\]

### Step 5: Solve for \(z\)
Divide both sides by \(14\):

\[
z = -\frac{37}{14}
\]

### Final Answer
\[
z = -\frac{37}{14}
\]

Would you like further details, or do you have any questions?

Here are some related questions:
1. How would the solution change if the constants were altered?
2. What are some methods to check if the solution to an equation is correct?
3. How can you solve similar equations with fractions in the original problem?
4. What techniques apply when equations involve only constants and no variables?
5. How would this solution differ if it involved inequalities instead of equalities?

**Tip:** Always double-check your distribution step, as small errors here can lead to incorrect solutions.

Step-by-step solution to solving the linear equation -6(z-3)-2 = -4(6+5z)+3. This solution covers algebraic concepts such as distribution, combining like terms, and isolating variables to find the final answer for z. Ideal for Grades 8-10.

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