To solve the equation \(-15 = -6(3 + x) + 4(x - 6)\), we will first expand and simplify the equation.

### Step 1: Expand the equation

Expand the terms on the right side of the equation:

\[
-15 = -6(3 + x) + 4(x - 6)
\]

Distribute \(-6\) and \(4\):

\[
-15 = -6 \cdot 3 - 6 \cdot x + 4 \cdot x - 4 \cdot 6
\]

This simplifies to:

\[
-15 = -18 - 6x + 4x - 24
\]

### Step 2: Combine like terms

Combine the constant terms \(-18\) and \(-24\), and the \(x\)-terms \(-6x\) and \(4x\):

\[
-15 = (-18 - 24) + (-6x + 4x)
\]

Simplifying further:

\[
-15 = -42 - 2x
\]

### Step 3: Solve for \(x\)

Add 42 to both sides to isolate the \(x\)-terms:

\[
-15 + 42 = -2x
\]

\[
27 = -2x
\]

Divide both sides by \(-2\):

\[
x = \frac{27}{-2}
\]

\[
x = -\frac{27}{2}
\]

\[
x = -13.5
\]

### Solution

The value of \(x\) is \(-13.5\).

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Would you like more details on any step or have any other questions?

Here are some related questions:
1. How do you solve equations with multiple variables?
2. What are the rules for distributing negative numbers in equations?
3. Can you solve an equation with fractions?
4. How do you handle equations with exponents?
5. What is the process for solving inequalities?

**Tip:** Always double-check your solution by substituting it back into the original equation to ensure it satisfies all terms.

Learn how to solve the equation -15 = -6(3 + x) + 4(x - 6) step-by-step. This problem involves equations with distribution and combining like terms. Suitable for high school students learning algebra.

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