Solve the equation by factoring. (Enter your answers as a comma-separated list.)
−4x2 − 6x + 4 = 0 slove for x 

The given quadratic equation is:

\[
-4x^2 - 6x + 4 = 0
\]

### Step 1: Simplify the equation
We can start by dividing the entire equation by \(-2\) to simplify it:

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

### Step 2: Factor the quadratic equation
We are looking for two numbers that multiply to \(2 \times (-2) = -4\) and add up to \(3\).

The numbers \(4\) and \(-1\) satisfy these conditions, because:

\[
4 \times (-1) = -4 \quad \text{and} \quad 4 + (-1) = 3
\]

Now, we can rewrite the middle term and factor by grouping:

\[
2x^2 + 4x - x - 2 = 0
\]

Group the terms:

\[
(2x^2 + 4x) - (x + 2) = 0
\]

Factor each group:

\[
2x(x + 2) - 1(x + 2) = 0
\]

Factor out the common binomial factor \((x + 2)\):

\[
(x + 2)(2x - 1) = 0
\]

### Step 3: Solve for \(x\)
Set each factor equal to 0:

1. \(x + 2 = 0 \quad \Rightarrow \quad x = -2\)
2. \(2x - 1 = 0 \quad \Rightarrow \quad x = \frac{1}{2}\)

### Final Answer:
The solutions are:

\[
x = -2, \frac{1}{2}
\]

Would you like further details or have any questions?

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Here are 5 related questions:
1. How can you check if your factored solution is correct?
2. What are other methods to solve a quadratic equation?
3. What is the quadratic formula, and how does it apply here?
4. How do you know when a quadratic equation cannot be factored?
5. What are the differences between factoring and completing the square?

**Tip:** Always simplify the quadratic equation by removing common factors before factoring.

Solve the equation by factoring. (Enter your answers as a comma-separated list.) −4x^2 − 6x + 4 = 0 solve for x

Learn how to solve the quadratic equation −4x^2 − 6x + 4 by factoring. This step-by-step solution includes simplifying the equation, factoring by grouping, and applying the Zero Product Property. Suitable for students in Grades 9-11.

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