How many solutions does this equation have? \[ -10-2(7 n-3)=-14 n \]

Let's analyze the given equation: \[ -10 - 2(7n - 3) = -14n \] **Step 1: Expand the Equation** First, distribute the \(-2\) across the terms inside the parentheses: \[ -10 - 14n + 6 = -14n \] **Step 2: Simplify the Left Side** Combine the constant terms: \[ (-10 + 6) - 14n = -14n \\ -4 - 14n = -14n \] **Step 3: Isolate the Variable** Add \(14n\) to both sides to eliminate the \(-14n\) term: \[ -4 = 0 \] **Step 4: Analyze the Result** The statement \(-4 = 0\) is a contradiction; it is never true. This means there is no value of \(n\) that can satisfy the original equation. **Conclusion:** The equation has **no solutions**. Answer: There is no solution; the equation cannot be satisfied by any real number.