If `(x − 2)(x+3) = x^(2) - 4`, the value of x is 

Options

A. 3
B. 2
C. `(1)/(2)`
D. `-2`

Answer

To solve the equation \((x - 2)(x + 3) = x^2 - 4\), we will follow these steps:

### Step 1: Expand the left side of the equation
We start by expanding the left-hand side \((x - 2)(x + 3)\).

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

### Step 2: Set the equation
Now, we set the expanded left side equal to the right side of the original equation:

\[ x^2 + x - 6 = x^2 - 4 \]

### Step 3: Simplify the equation
Next, we subtract \(x^2\) from both sides of the equation:

\[ x - 6 = -4 \]

### Step 4: Solve for \(x\)
Now, we will isolate \(x\) by adding 6 to both sides:

\[ x = -4 + 6 \]
\[ x = 2 \]

### Final Answer
Thus, the value of \(x\) is \(2\).

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