To solve the quadratic equation \(-7x^2 + 14x + 21 = 0\), we can start by simplifying it.

### Step 1: Simplify the Equation
First, divide the entire equation by \(-7\) to make the coefficient of \(x^2\) positive:

\[
x^2 - 2x - 3 = 0
\]

### Step 2: Factor the Quadratic
Now, factor the quadratic equation:

\[
(x - 3)(x + 1) = 0
\]

### Step 3: Solve for \(x\)
Set each factor equal to zero:

\[
x - 3 = 0 \quad \text{or} \quad x + 1 = 0
\]

So, the solutions are:

\[
x = 3 \quad \text{or} \quad x = -1
\]

Thus, the solutions to the equation are \(x = 3\) and \(x = -1\).

Would you like further details or have any questions?

Here are five related questions for further exploration:

1. How do you solve a quadratic equation using the quadratic formula?
2. What is the discriminant of a quadratic equation and how is it used?
3. Can all quadratic equations be factored easily?
4. How can you determine the vertex of the parabola represented by a quadratic equation?
5. How do the solutions of a quadratic equation relate to the graph of the corresponding function?

**Tip:** Always check if a quadratic equation can be factored easily before using more complex methods like the quadratic formula.

Learn how to solve the quadratic equation -7x^2 + 14x + 21 with a detailed step-by-step solution. This problem covers key algebraic concepts, including factoring quadratic equations and solving linear equations. Suitable for students in Grades 7-9.

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