To solve the equation \(z^2 - 12 = 4z\) using factoring, let's follow these steps:

### Step-by-Step Solution

1. **Rewrite the equation:**

   Start by rewriting the equation to set it equal to 0:
   \[
   z^2 - 12 = 4z
   \]

   Subtract \(4z\) from both sides:
   \[
   z^2 - 4z - 12 = 0
   \]

2. **Factor the quadratic equation:**

   We need to factor the quadratic expression \(z^2 - 4z - 12\). To factor this, look for two numbers that multiply to \(-12\) (the constant term) and add to \(-4\) (the coefficient of \(z\)).

   The two numbers that satisfy these conditions are \(-6\) and \(2\), because:
   \[
   -6 \times 2 = -12 \quad \text{and} \quad -6 + 2 = -4
   \]

   Thus, we can factor the quadratic expression as:
   \[
   (z - 6)(z + 2) = 0
   \]

3. **Set each factor equal to zero:**

   For the product to be zero, at least one of the factors must be zero. So, set each factor equal to zero and solve for \(z\):
   \[
   z - 6 = 0 \quad \text{or} \quad z + 2 = 0
   \]

4. **Solve for \(z\):**

   Solving these equations gives:
   \[
   z = 6 \quad \text{or} \quad z = -2
   \]

### Solutions

The solutions to the equation \(z^2 - 12 = 4z\) are:
\[
z = 6 \quad \text{and} \quad z = -2
\]

Would you like more details or have any questions?

### Related Questions

1. How do you solve a quadratic equation using the quadratic formula?
2. What is the process for completing the square to solve \(z^2 - 12 = 4z\)?
3. How do you determine the vertex and axis of symmetry for the quadratic equation \(z^2 - 4z - 12 = 0\)?
4. Can you solve the equation \(z^2 - 12z + 36 = 4z - 24\) by factoring?
5. What are the differences between solving a quadratic equation by factoring, completing the square, and using the quadratic formula?

### Tip

When factoring a quadratic equation, always check your factors by expanding them to ensure they multiply back to the original quadratic expression.

Learn how to solve the quadratic equation z^2 - 12 = 4z using factoring with a detailed step-by-step solution. This problem involves factoring quadratic equations and is suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation