Solve: `5(x-1)+2(x+3)+6=0`. Check the result.

Answer

To solve the equation \( 5(x-1) + 2(x+3) + 6 = 0 \), we will follow these steps:

### Step 1: Distribute the terms inside the parentheses
We start by distributing the coefficients \(5\) and \(2\) into the expressions inside the parentheses.

\[ 5(x-1) = 5x - 5 \]
\[ 2(x+3) = 2x + 6 \]

Now, substituting these back into the equation gives us:

\[ 5x - 5 + 2x + 6 + 6 = 0 \]

### Step 2: Combine like terms
Next, we combine the \(x\) terms and the constant terms.

\[ (5x + 2x) + (-5 + 6 + 6) = 0 \]
\[ 7x + 7 = 0 \]

### Step 3: Isolate the variable \(x\)
To isolate \(x\), we first move the constant term to the other side of the equation.

\[ 7x = -7 \]

### Step 4: Solve for \(x\)
Now, we divide both sides by \(7\) to solve for \(x\).

\[ x = \frac{-7}{7} = -1 \]

### Step 5: Check the result
To verify our solution, we substitute \(x = -1\) back into the original equation:

\[ 5(-1 - 1) + 2(-1 + 3) + 6 = 0 \]
Calculating each term:
\[ 5(-2) + 2(2) + 6 = 0 \]
\[ -10 + 4 + 6 = 0 \]
\[ -10 + 10 = 0 \]
\[ 0 = 0 \]

Since both sides of the equation are equal, our solution is confirmed.

### Final Answer:
The solution to the equation is \( x = -1 \).

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